Over the past two and a half decades, covariance intersection (CI) has provided a means for robust estimation in scenarios where the uncertainty information is incomplete. Estimation in distributed and decentralized data fusion (DDF) settings is typically characterized by having nonzero cross-correlations between the estimates to be merged. Mean-square-error (MSE) optimal estimators, such as the Kalman filter (KF), are limited to data fusion problems where these cross-correlations are fully known. Keeping track of cross-correlations is unfortunately not always possible. To quantify confidence in the estimate’s uncertainty, the concept of conservativeness has been introduced. A conservative estimator guarantees that the computed covariance matrix is not smaller than the actual covariance matrix. It turns out that CI guarantees conservativeness for any degree of unknown cross-correlations as long as the estimates to be fused are conservative. It should be noted that, in the CI literature, the notion of covariance consistency is often used to characterize conservativeness . In this work, we use the latter term.
@article{CSM24_Forsling,
title = {{A Quarter Century of Covariance Intersection: Correlations Still Unknown?}},
author = {Robin Forsling and Benjamin Noack and Gustaf Hendeby},
doi = {10.1109/MCS.2024.3358658},
issue = {2},
journal = {IEEE Control Systems Magazine},
month = apr,
pages = {81--105},
volume = {44},
year = {2024}
}
Conferences
Fabio Broghammer, Thomas Wiedemann, Siwei Zhang, Benjamin Noack
Simultaneous Gas Exploration and Network Localization with Robotic Swarms (to appear) Proceedings of the IEEE ICASSP 2024 2nd Workshop on Signal Processing for Autonomous Systems, Seoul, Republic of Korea, April, 2024.
abstract
BibTeX
A common issue in state-of-the-art robotic gas distribution mapping and gas source localization is the fact that the positions of the robots are assumed to be perfectly known and the position uncertainties are not considered in movement strategies. However, for cooperative mobile sensor networks with relative localization systems, the geometry of the network plays an important role for localization accuracy. In this paper, we introduce the problem of Simultaneous Exploration and Localization (SEAL). Our approach incorporates position uncertainties of gas concentration measurements into the estimation of environment features, such as a source position or wind direction, and exploits the position uncertainties to design an exploration strategy for sampling gas distributions with mobile robots. More precisely, the paper presents a swarm control algorithm that improves the estimation by adapting the swarm formation for better localization. In simulations, we analyze how position uncertainties affect estimation and exploration performance and we compare the presented control algorithm with a method unaware of position uncertainties.
@inproceedings{ICASSP24_Workshop_Broghammer,
title = {{Simultaneous Gas Exploration and Network Localization with Robotic Swarms (to appear)}},
author = {Fabio Broghammer and Thomas Wiedemann and Siwei Zhang and Benjamin Noack},
booktitle = {Proceedings of the IEEE ICASSP 2024 2nd Workshop on Signal Processing for Autonomous Systems},
address = {Seoul, Republic of Korea},
month = apr,
year = {2024}
}
Other
Christopher Funk, Benjamin Noack
An Event-Based Approach for the Conservative Compression of Covariance Matrices arXiv, 2024.
This work introduces a flexible and versatile method for the data-efficient yet conservative transmission of covariance matrices, where a matrix element is only transmitted if a so-called triggering condition is satisfied for the element. Here, triggering conditions can be parametrized on a per-element basis, applied simultaneously to yield combined triggering conditions or applied only to certain subsets of elements. This allows, e.g., to specify transmission accuracies for individual elements or to constrain the bandwidth available for the transmission of subsets of elements. Additionally, a methodology for learning triggering condition parameters from an application-specific dataset is presented. The performance of the proposed approach is quantitatively assessed in terms of data reduction and conservativeness using estimate data derived from real-world vehicle trajectories from the InD-dataset, demonstrating substantial data reduction ratios with minimal over-conservativeness. The feasibility of learning triggering condition parameters is demonstrated.
@misc{arXiv2024_Funk,
title = {{An Event-Based Approach for the Conservative Compression of Covariance Matrices}},
author = {Christopher Funk and Benjamin Noack},
copyright = {Creative Commons Attribution 4.0 International},
doi = {10.48550/ARXIV.2403.05977},
keywords = {Robotics (cs.RO), Artificial Intelligence (cs.AI), FOS: Computer and information sciences, FOS: Computer and information sciences},
publisher = {arXiv},
year = {2024}
}
2023
Journal Articles
Marco Ristic, Benjamin Noack, Uwe D. Hanebeck
Distributed Range-Only Localisation that Preserves Sensor and Navigator Privacies IEEE Transactions on Automatic Control, vol. 68, pp. 7151–7163, December, 2023.
Distributed state estimation and localisation methods have become increasingly popular with the rise of ubiquitous computing, and have led naturally to an increased concern regarding data and estimation privacy. Traditional distributed sensor navigation methods typically involve the leakage of sensor or navigator information by communicating measurements or estimates and thus do not preserve participants' privacy. The existing approaches that do provide such guarantees fail to address sensor and navigator privacy in the common application of model-based range-only localisation, consequently forfeiting broad applicability. In this work, we define a notion of privacy-preserving linear combination aggregation and use it to derive a modified Extended Kalman Filter using range measurements such that navigator location, sensors' locations, and sensors' measurements are kept private during navigation. Additionally, a formal cryptographic backing is presented to guarantee our method's privacy as well as an implementation to evaluate its performance. The novel, provably secure, range-based localisation method has applications in a variety of environments where sensors may not be trusted or estimates are considered sensitive, such as autonomous vehicle localisation or air traffic navigation.
@article{TAC23_Ristic,
title = {{Distributed Range-Only Localisation that Preserves Sensor and Navigator Privacies}},
author = {Marco Ristic and Benjamin Noack and Uwe D. Hanebeck},
doi = {10.1109/TAC.2023.3263740},
issue = {12},
journal = {IEEE Transactions on Automatic Control},
month = dec,
pages = {7151--7163},
volume = {68},
year = {2023}
}
Tobias Schlagenhauf, Yiwen Lin, Benjamin Noack
Discriminative Feature Learning Through Feature Distance Loss Machine Vision and Applications, vol. 34, no. 25, January, 2023.
Ensembles of convolutional neural networks have shown remarkable results in learning discriminative semantic features for image classification tasks. However, the models in the ensemble often concentrate on similar regions in images. This work proposes a novel method that forces a set of base models to learn different features for a classification task. These models are combined in an ensemble to make a collective classification. The key finding is that by forcing the models to concentrate on different features, the classification accuracy is increased. To learn different feature concepts, a so-called feature distance loss is implemented on the feature maps. The experiments on benchmark convolutional neural networks (VGG16, ResNet, AlexNet), popular datasets (Cifar10, Cifar100, miniImageNet, NEU, BSD, TEX), and different training samples (3, 5, 10, 20, 50, 100 per class) show the effectiveness of the proposed feature loss. The proposed method outperforms classical ensemble versions of the base models. The Class Activation Maps explicitly prove the ability to learn different feature concepts. The code is available at: https://github.com/2Obe/Feature-Distance-Loss.git.
@article{MVA23_Schlagenhauf,
title = {{Discriminative Feature Learning Through Feature Distance Loss}},
author = {Tobias Schlagenhauf and Yiwen Lin and Benjamin Noack},
doi = {10.1007/s00138-023-01379-1},
journal = {Machine Vision and Applications},
month = jan,
number = {25},
volume = {34},
year = {2023}
}
Johannes Westermann, Jana Mayer, Janko Petereit, Benjamin Noack
Receding Horizon Cost-Aware Adaptive Sampling for Environmental Monitoring IEEE Control Systems Letters, vol. 7, pp. 1069–1074, January, 2023.
In this letter, environmental monitoring by mobile robots is considered where expensive or time-consuming sampling has to be carried out in order to obtain a metamodel of the phenomenon investigated. Due to limited resources, often not only a limited number of samples can be taken, but also the cost and time of the traveled distance between the sample points must be considered. We present an adaptive sampling method that greatly reduces the robot’s travel costs for all common sampling criteria with minimal impact on model accuracy. This is achieved by predicting future sample points based on virtual sampling over a horizon in each iteration of the algorithm and suggesting a next sample point after a cost optimization. The algorithm is simulatively evaluated for application to global exploration and reconstruction of unknown phenomena on a variety of randomly generated phenomena. It is shown that our method vastly outperforms standard adaptive sampling.
@article{LCSS23_Westermann,
title = {{Receding Horizon Cost-Aware Adaptive Sampling for Environmental Monitoring}},
author = {Johannes Westermann and Jana Mayer and Janko Petereit and Benjamin Noack},
doi = {10.1109/LCSYS.2022.3230058},
journal = {IEEE Control Systems Letters},
month = jan,
pages = {1069--1074},
volume = {7},
year = {2023}
}
Conferences
Eva Julia Schmitt, Benjamin Noack
Event-based Colored-Noise Kalman Filtering for Improved Resource Efficiency Proceedings of the combined IEEE 2023 Symposium Sensor Data
Fusion and International Conference on Multisensor Fusion and
Integration (SDF-MFI 2023), Bonn, Germany, November, 2023.
In modern automated systems, the number of agents and sensors is rapidly increasing and with them the energy consumption and the burden on communications networks. One way to increase the energy and spectral efficiency in sensor networks is to replace periodic transmissions between nodes with event-based transmissions and to use matching estimation techniques at the receiving nodes. Since multi-sensor systems and smart event-trigger designs often lead to correlations between measurements due to correlated process and measurement noise, estimators that can handle such correlations are required to guarantee good performance. In this paper, an event-based colored-noise Kalman filter was developed and specifically designed for a finite impulse response-based stochastic trigger. Nevertheless, the concept is suitable for a wide class of correlated input data.
@inproceedings{MFI23_Schmitt,
title = {{Event-based Colored-Noise Kalman Filtering for Improved Resource Efficiency}},
author = {Eva Julia Schmitt and Benjamin Noack},
booktitle = {Proceedings of the combined IEEE 2023 Symposium Sensor Data
Fusion and International Conference on Multisensor Fusion and
Integration (SDF-MFI 2023)},
address = {Bonn, Germany},
doi = {10.1109/SDF-MFI59545.2023.10361406},
month = nov,
year = {2023}
}
Jindřich Duník, Ondřej Straka, Benjamin Noack
Classification of Uncertainty Sources for Reliable
Bayesian Estimation Proceedings of the combined IEEE 2023 Symposium Sensor Data
Fusion and International Conference on Multisensor Fusion and
Integration (SDF-MFI 2023), Bonn, Germany, November, 2023.
Recursive Bayesian estimation has emerged as a key tool for estimating the unknown state of a system. The wide range of applications has resulted in a correspondingly wide variety of estimation algorithms. The Kalman filter and its derivatives, like extended and unscented Kalman filters, are the most prominent examples, while non-Gaussian full-blown filters are on the rise with the increasing availability of computational power. The filtering results are naturally accompanied by an assessment of the estimate's uncertainty. However, this assessment may mislead the user into believing that the estimate is reliable, i.e., that the uncertainty reported by the filter matches the actual uncertainty. For a filter to assess its uncertainty correctly, often strict requirements must be met. The misalignment can be attributed to different origins, for which this work proposes a classification covering different stages of a filter design. Approximations and assumptions made in each class impair the filter's reliability. This paper provides a conceptual perspective on how reliability can be defined and how it can be assessed. An example of a reliability index is examined in a simulated scenario to illustrate how it can contribute to a better understanding of the overall performance of a filter.
@inproceedings{MFI23_Dunik,
title = {{Classification of Uncertainty Sources for Reliable
Bayesian Estimation}},
author = {Jind{\v r}ich Dun{\'\i}k and Ond{\v r}ej Straka and Benjamin Noack},
booktitle = {Proceedings of the combined IEEE 2023 Symposium Sensor Data
Fusion and International Conference on Multisensor Fusion and
Integration (SDF-MFI 2023)},
address = {Bonn, Germany},
doi = {10.1109/SDF-MFI59545.2023.10361300},
month = nov,
year = {2023}
}
Jana Mayer, Vesa Klumpp, Jonas Hillenbrand, Benjamin Noack
Statistical Approach for Preload Monitoring of Ball Screw Drives Proceedings of the IEEE SENSORS 2023 Conference, Vienna, Austria, October, 2023.
Preload loss is one of the most frequent causes of ball screw drive failures. To avoid a reduction in production quality or sudden machine breakdowns, condition monitoring systems are of interest. One method to observe the preload conditions is the use of strain gauge sensors embedded in the nut. Evaluating the strain signal, we show that a loss of preload is associated with irregular motion of the balls. Based on that, a novel statistical method to characterize the smoothness of the balls' motion is introduced. The approach results in a health value, which is directly associated with the preload condition of the ball screw.
@inproceedings{SENSORS23_Mayer,
title = {{Statistical Approach for Preload Monitoring of Ball Screw Drives}},
author = {Jana Mayer and Vesa Klumpp and Jonas Hillenbrand and Benjamin Noack},
booktitle = {Proceedings of the IEEE SENSORS 2023 Conference},
address = {Vienna, Austria},
doi = {10.1109/SENSORS56945.2023.10325060},
month = oct,
year = {2023}
}
Ofer Dagan, Christopher Funk, Nisar R. Ahmed, Benjamin Noack
Exploiting Structure for Optimal Multi-Agent Bayesian Decentralized Estimation (to appear) Workshop on Inference and Decision Making for Autonomous Vehicles as Robotics: Science and Systems (RSS 2023), Daegu, Republic of Korea, July, 2023.
BibTeX
@inproceedings{RSS23_Dagan,
title = {{Exploiting Structure for Optimal Multi-Agent Bayesian Decentralized Estimation (to appear)}},
author = {Ofer Dagan and Christopher Funk and Nisar R. Ahmed and Benjamin Noack},
booktitle = {Workshop on Inference and Decision Making for Autonomous Vehicles as Robotics: Science and Systems (RSS 2023)},
address = {Daegu, Republic of Korea},
month = jul,
year = {2023}
}
Christopher Funk, Benjamin Noack
Conservative Data Reduction for Covariance Matrices Using Elementwise Event Triggers Proceedings of the 26th International Conference on Information Fusion (Fusion 2023), Charleston, South Carolina, USA, July, 2023.
Decentralized data fusion algorithms are fundamentally built on the exchange of estimates and covariance matrices between the individual components. This leads to a high volume of data, mainly caused by the covariance matrices, which can be problematic, especially in environments with limited bandwidth. In order to guarantee the proper functioning of decentralized estimation algorithms, data reduction methods for covariance matrices must ensure that the reduced matrices are conservative, i.e., do not underestimate the actual uncertainty. Motivated by these considerations, this paper presents an elementwise event-triggered method for the data-reduced transmission of covariance matrices that takes into account the aforementioned condition concerning uncertainty. For this purpose, several event triggers are proposed and, based on the event data and diagonal dominance, upper bounds for the actual covariance matrices are derived. An investigation of the data reduction and its influence on the estimation results is performed in a decentralized tracking scenario. The results show that substantial data reduction is possible with only minor losses in estimation quality.
@inproceedings{Fusion23_Funk,
title = {{Conservative Data Reduction for Covariance Matrices Using Elementwise Event Triggers}},
author = {Christopher Funk and Benjamin Noack},
booktitle = {Proceedings of the 26th International Conference on Information Fusion (Fusion 2023)},
address = {Charleston, South Carolina, USA},
doi = {10.23919/FUSION52260.2023.10224214},
month = jul,
year = {2023}
}
Anne Rother, Gunther Notni, Alexander Hasse, Benjamin Noack, Christian Beyer, Jan Reißmann, Chen Zhang, Marco Ragni, Julia C. Arlinghaus, Myra Spiliopoulou
Productive Teaming Under Uncertainty: When a Human and a Machine Classify Objects Together Proceedings of the 2023 IEEE International Conference on Advanced Robotics and its Social Impacts (ARSO 2023), Berlin, Germany, June, 2023.
We study the task of object categorization in an industrial setting. Typically, a machine classifies objects according to an internal, inferred model, and calls to a human worker if it is uncertain. However, the human worker may be also uncertain. We elaborate on the challenges and solutions to assess the certainty of the human without disturbing the industrial process, and to assess label reliability and human certainty in conventional object classification and crowdworking. Albeit there are methods for measuring stress, insights on the correlation of stress and uncertainty and uncertainty indicators during labeling by humans, these advances are yet to be combined to solve the aforementioned uncertainty challenge. We propose a solution as a sequence of tasks, starting with a experiment that measures human certainty in a task of controlled difficulty, whereupon we can associate certainty with correctness and levels of vital signals.
@inproceedings{ARSO23_Rother,
title = {{Productive Teaming Under Uncertainty: When a Human and a Machine Classify Objects Together}},
author = {Anne Rother and Gunther Notni and Alexander Hasse and Benjamin Noack and Christian Beyer and Jan Rei{\ss}mann and Chen Zhang and Marco Ragni and Julia C. Arlinghaus and Myra Spiliopoulou},
booktitle = {Proceedings of the 2023 IEEE International Conference on Advanced Robotics and its Social Impacts (ARSO 2023)},
address = {Berlin, Germany},
doi = {10.1109/ARSO56563.2023.10187430},
month = jun,
year = {2023}
}
Christopher Funk, Benjamin Noack
Graduated Moving Window Optimization as a Flexible Framework for Multi-Object Tracking Proceedings of the 2023 American Control Conference (ACC 2023), San Diego, California, USA, June, 2023.
Continuous optimization methods for multiple object tracking allow to jointly estimate continuous object trajectories and perform implicit data association. However, the local minima that arise from including data association in a continuous optimization problem pose challenges. In addition, optimization is usually performed either over a fixed or an indefinitely growing time frame. This either discards valuable past information or is computationally unsustainable. Hence, in this work, a flexible continuous optimization based framework for multiple object tracking that accounts for these issues is proposed. The framework provides a unified approach to not only include data association, but also multiple motion models and temporary interactions between objects in a continuous optimization problem. It leverages the concept of graduated optimization, a heuristic, which allows avoiding local minima. The proposed framework's performance is benchmarked on a synthetic dataset, showing its capabilities and indicating areas of possible improvement.
@inproceedings{ACC23_Funk,
title = {{Graduated Moving Window Optimization as a Flexible Framework for Multi-Object Tracking}},
author = {Christopher Funk and Benjamin Noack},
booktitle = {Proceedings of the 2023 American Control Conference (ACC 2023)},
address = {San Diego, California, USA},
doi = {10.23919/ACC55779.2023.10156509},
month = jun,
year = {2023}
}
Other
Christopher Funk, Ofer Dagan, Benjamin Noack, Nisar R. Ahmed
Exploiting Structure for Optimal Multi-Agent Bayesian Decentralized Estimation arXiv, 2023.
A key challenge in Bayesian decentralized data fusion is the `rumor propagation' or `double counting' phenomenon, where previously sent data circulates back to its sender. It is often addressed by approximate methods like covariance intersection (CI) which takes a weighted average of the estimates to compute the bound. The problem is that this bound is not tight, i.e. the estimate is often over-conservative. In this paper, we show that by exploiting the probabilistic independence structure in multi-agent decentralized fusion problems a tighter bound can be found using (i) an expansion to the CI algorithm that uses multiple (non-monolithic) weighting factors instead of one (monolithic) factor in the original CI and (ii) a general optimization scheme that is able to compute optimal bounds and fully exploit an arbitrary dependency structure. We compare our methods and show that on a simple problem, they converge to the same solution. We then test our new non-monolithic CI algorithm on a large-scale target tracking simulation and show that it achieves a tighter bound and a more accurate estimate compared to the original monolithic CI.
@misc{arXiv2023_Funk,
title = {{Exploiting Structure for Optimal Multi-Agent Bayesian Decentralized Estimation}},
author = {Christopher Funk and Ofer Dagan and Benjamin Noack and Nisar R. Ahmed},
copyright = {Creative Commons Attribution 4.0 International},
doi = {10.48550/ARXIV.2307.10594},
keywords = {Robotics (cs.RO), Artificial Intelligence (cs.AI), FOS: Computer and information sciences, FOS: Computer and information sciences},
publisher = {arXiv},
year = {2023}
}
Anne Rother, Gunther Notni, Alexander Hasse, Benjamin Noack, Christian Beyer, Jan Reißmann, Chen Zhang, Marco Ragni, Julia Arlinghaus, Myra Spiliopoulou
Human Uncertainty in Interaction With a Machine: Establishing a Reference Dataset Proceedings of the 60th Ilmenau Scientific Colloquium: Engineering for a Changing World, Ilmenau, Germany, September, 2023.
We investigate the task of malformed object classification in an industrial setting, where the term 'malformed' encompasses objects that are misshapen, distorted, corroded or broken. Recognizing whether such an object can be repaired, taken apart so that its components can be used otherwise, or dispatched for recycling, is a difficult classification task. Despite the progress of artificial intelligence for the classification of objects based on images, the classification of malformed objects still demands human involvement, because each such object is unique. Ideally, the intelligent machine should demand expert support only when it is uncertain about the class. But what if the human is also uncertain? Such a case must be recognized before being dealt with. Goal of this research thread is to establish a reference dataset on human uncertainty for such a classification problem and to derive indicators of uncertainty from sensory inputs. To this purpose, we designed an experiment for an object classification scenario where the uncertainty can be directly linked to the difficulty of labelling each object. By thus controlling uncertainty, we intend to build up a reference dataset and investigate how different sensory inputs can serve as uncertainty indicators for these data.
@inproceedings{ISC23_Rother,
title = {{Human Uncertainty in Interaction With a Machine: Establishing a Reference Dataset}},
author = {Anne Rother and Gunther Notni and Alexander Hasse and Benjamin Noack and Christian Beyer and Jan Rei{\ss}mann and Chen Zhang and Marco Ragni and Julia Arlinghaus and Myra Spiliopoulou},
booktitle = {Proceedings of the 60th Ilmenau Scientific Colloquium: Engineering for a Changing World},
address = {Ilmenau, Germany},
copyright = {Creative Commons Attribution 4.0 International},
doi = {10.22032/dbt.58928},
month = sep,
year = {2023}
}
Benjamin Noack, Florian Röhrbein, Gunter Notni
Event-Based Sensor Fusion in Human-Machine Teaming Proceedings of the 60th Ilmenau Scientific Colloquium: Engineering for a Changing World, Ilmenau, Germany, September, 2023.
Realizing intelligent production systems where machines and human workers can team up seamlessly demands a yet unreached level of situational awareness. The machines' leverage to reach such awareness is to amalgamate a wide variety of sensor modalities through multisensor data fusion. A particularly promising direction to establishing human-like collaborations can be seen in the use of neuro-inspired sensing and computing technologies due to their resemblance with human cognitive processing. This note discusses the concept of integrating neuromorphic sensing modalities into classical sensor fusion frameworks by exploiting event-based fusion and filtering methods that combine time-periodic process models with event-triggered sensor data. Event-based sensor fusion hence adopts the operating principles of event-based sensors and even exhibits the ability to extract information from absent data. Thereby, it can be an enabler to harness the full information potential of the intrinsic spiking nature of event-driven sensors.
@inproceedings{ISC23_Noack,
title = {{Event-Based Sensor Fusion in Human-Machine Teaming}},
author = {Benjamin Noack and Florian R{\"o}hrbein and Gunter Notni},
booktitle = {Proceedings of the 60th Ilmenau Scientific Colloquium: Engineering for a Changing World},
address = {Ilmenau, Germany},
copyright = {Creative Commons Attribution 4.0 International},
doi = {10.22032/dbt.58924},
keywords = {Sensor Fusion, Neuromorphic Sensors, Event-Based Filtering},
month = sep,
year = {2023}
}
2022
Conferences
Marco Ristic, Benjamin Noack
Privileged Estimate Fusion With Correlated Gaussian Keystreams Proceedings of the 61th IEEE Conference on Decision and Control (CDC 2022), Cancún, Mexico, December, 2022.
Providing cryptographic privacy guarantees in a distributed state estimation problem has been a growing topic of research since the ubiquity of modern public networks. One such guarantee is having different levels of estimation performance achievable by trusted and untrusted users within a sensor network. In the presence of multiple sensor measurements, guaranteeing better estimation performance by the usual means of adding removable noise to measurements is complicated by an alternative for untrusted users to improve their performance: fusing more measurements. Our novel method adds correlated noise to different sensors, restricting the performance gained from fusing additional measurements while guaranteeing better performance to those that can remove it. We extend a cryptographic framework for defining estimation privilege and use this to prove the scheme’s security goals, while simulations demonstrate the effects of parameters in a concrete estimation scenario. A scheme that can ensure such differences in estimation performance between estimators of differing privileges can find applications in priority-based or subscription-based estimation performances in environments where more than one sensor is present.
@inproceedings{CDC22_Ristic,
title = {{Privileged Estimate Fusion With Correlated Gaussian Keystreams}},
author = {Marco Ristic and Benjamin Noack},
booktitle = {Proceedings of the 61th IEEE Conference on Decision and Control (CDC 2022)},
address = {Canc{\'u}n, Mexico},
doi = {10.1109/CDC51059.2022.9993240},
month = dec,
year = {2022}
}
Marco Ristic, Benjamin Noack
Encrypted Fast Covariance Intersection Without Leaking Fusion Weights Proceedings of the 2022 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI 2022), Cranfield, United Kingdom, September, 2022.
State estimate fusion is a common requirement in distributed sensor networks and can be complicated by untrusted participants or network eavesdroppers. We present a method for computing the common Fast Covariance Intersection fusion algorithm on an untrusted cloud without disclosing individual estimates or the fused result. In an existing solution to this problem, fusion weights corresponding to the sensor estimate errors are leaked to the cloud to perform the fusion. In this work, we present a method that guarantees no leakage at the cloud by requiring an additional computation step by the party querying the cloud for the fused result. The Paillier encryption scheme is used to homomorphically compute separate parts of the computation that can be combined after decryption. This encrypted Fast Covariance Intersection algorithm can be used in scenarios where the fusing cloud is not trusted and any information on sensor performances must remain confidential.
@inproceedings{MFI22_Ristic,
title = {{Encrypted Fast Covariance Intersection Without Leaking Fusion Weights}},
author = {Marco Ristic and Benjamin Noack},
booktitle = {Proceedings of the 2022 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI 2022)},
address = {Cranfield, United Kingdom},
doi = {10.1109/MFI55806.2022.9913840},
month = sep,
year = {2022}
}
Benjamin Noack, Clemens Öhl, Uwe D. Hanebeck
Event-Based Kalman Filtering Exploiting Correlated Trigger Information Proceedings of the 25th International Conference on Information Fusion (Fusion 2022), Linköping, Sweden, July, 2022.
In networked estimation architectures, event-based sensing and communication can contribute to a more efficient resource allocation in general, and improved utilization of communication resources, in particular. In order to tap the full potential of event-based scheduling, the design of transmission triggers and estimators need to be closely coupled while two directions are promising: First, the remote estimator can exploit the absence of transmissions and translate it into implicit information about the sensor data. Second, an intelligent trigger mechanism at the sensor that predicts future sensor readings can decrease transmission rates while rendering the implicit information more valuable. Such an intelligent trigger has been developed in a recent paper based on a Finite Impulse Response filter, which requires the sensor to transmit an additional estimate alongside the measurement. In the present paper, the communication demand is further reduced by only transmitting the estimate. The remote estimator exploits correlations to incorporate the received information. In doing so, the estimation quality is also improved, which is confirmed by simulations.
@inproceedings{Fusion22_Noack,
title = {{Event-Based Kalman Filtering Exploiting Correlated Trigger Information}},
author = {Benjamin Noack and Clemens {\"O}hl and Uwe D. Hanebeck},
booktitle = {Proceedings of the 25th International Conference on Information Fusion (Fusion 2022)},
address = {Link{\"o}ping, Sweden},
doi = {10.23919/FUSION49751.2022.9841364},
month = jul,
year = {2022}
}
2021
Journal Articles
Susanne Radtke, Benjamin Noack, Uwe D. Hanebeck
Fully Decentralized Estimation Using Square-Root Decompositions Journal of Advances in Information Fusion, vol. 16, no. 1, pp. 3–16, June, 2021.
Networks consisting of several spatially distributed sensor nodes
are useful in many applications. While distributed information processing can be more robust and flexible than centralized filtering, it requires careful consideration of dependencies between local state estimates.This paper proposes an algorithm to keep track of dependencies in decentralized systems where no dedicated fusion center is present. Specifically, it addresses double-counting of measurement information due to intermediate fusion results and correlations due to common process noise and common prior information. To limit the necessary amount of data, this paper introduces a method to partially bound correlations, leading to a more conservative fusion result than the optimal reconstruction while reducing the necessary amount of data. Simulation studies compare the performance and convergence rate of the proposed algorithm to other state-of-the-art methods.
@article{JAIF21_Radtke,
title = {{Fully Decentralized Estimation Using Square-Root Decompositions}},
author = {Susanne Radtke and Benjamin Noack and Uwe D. Hanebeck},
journal = {Journal of Advances in Information Fusion},
month = jun,
number = {1},
pages = {3--16},
url = {https://confcats_isif.s3.amazonaws.com/web-files/journals/entries/3-16.pdf},
volume = {16},
year = {2021}
}
Marko Ristic, Benjamin Noack, Uwe D. Hanebeck
Cryptographically Privileged State Estimation With Gaussian Keystreams IEEE Control Systems Letters, vol. 6, pp. 602–607, May, 2021.
State estimation via public channels requires additional planning with regards to state privacy and information leakage of involved parties. In some scenarios, it is desirable to allow partial leakage of state information, thus distinguishing between privileged and unprivileged estimators and their capabilities. Existing methods that make this distinction typically result in reduced estimation quality, require additional communication channels, or lack a formal cryptographic backing. We introduce a method to decrease estimation quality at an unprivileged estimator using a stream of pseudorandom Gaussian samples while leaving privileged estimation unaffected and requiring no additional transmission beyond an initial key exchange. First, a cryptographic definition of privileged estimation is given, capturing the difference between privileges, before a privileged estimation scheme meeting the security notion is presented. Achieving cryptographically privileged estimation without additional channel requirements allows quantifiable estimation to be made available to the public while keeping the best estimation private to trusted privileged parties and can find uses in a variety of service-providing and privacy-preserving scenarios.
@article{LCSS21_Ristic_privileged,
title = {{Cryptographically Privileged State Estimation With Gaussian Keystreams}},
author = {Marko Ristic and Benjamin Noack and Uwe D. Hanebeck},
doi = {10.1109/LCSYS.2021.3084405},
issn = {2475-1456},
journal = {IEEE Control Systems Letters},
month = may,
pages = {602--607},
volume = {6},
year = {2021}
}
Christopher Funk, Benjamin Noack, Uwe D. Hanebeck
Conservative Quantization of Covariance Matrices with Applications to Decentralized Information Fusion Sensors, vol. 21, no. 9, April, 2021.
Information fusion in networked systems poses challenges with respect to both theory and implementation. Limited available bandwidth can become a bottleneck when high-dimensional estimates and associated error covariance matrices need to be transmitted. Compression of estimates and covariance matrices can endanger desirable properties like unbiasedness and may lead to unreliable fusion results. In this work, quantization methods for estimates and covariance matrices are presented and their usage with the optimal fusion formulas and covariance intersection is demonstrated. The proposed quantization methods significantly reduce the bandwidth required for data transmission while retaining unbiasedness and conservativeness of the considered fusion methods. Their performance is evaluated using simulations, showing their effectiveness even in the case of substantial data reduction.
@article{Sensors21_Funk,
title = {{Conservative Quantization of Covariance Matrices with Applications to Decentralized Information Fusion}},
author = {Christopher Funk and Benjamin Noack and Uwe D. Hanebeck},
doi = {10.3390/s21093059},
issn = {1424-8220},
journal = {Sensors},
month = apr,
number = {9},
url = {https://www.mdpi.com/1424-8220/21/9/3059},
volume = {21},
year = {2021}
}
Marko Ristic, Benjamin Noack, Uwe D. Hanebeck
Secure Fast Covariance Intersection Using Partially Homomorphic and Order Revealing Encryption Schemes IEEE Control Systems Letters, vol. 5, no. 1, pp. 217–222, January, 2021.
Fast covariance intersection is a widespread technique for state estimate fusion in sensor networks when cross-correlations are not known and fast computations are desired. The common requirement of sending estimates from one party to another during fusion forfeits local privacy. Current secure fusion algorithms rely on encryption schemes that do not provide sufficient flexibility. As a result, excess communication between estimate producers is required, which is often undesirable. We propose a novel method of homomorphically computing the fast covariance intersection algorithm on estimates encrypted with a combination of encryption schemes. Using order revealing encryption, we show how an approximate solution to the fast covariance intersection weights can be computed and combined with partially homomorphic encryptions of estimates, to calculate an encryption of the fused result. The described approach allows secure fusion of any number of private estimates, making third-party cloud processing a viable option when working with sensitive state estimates or when performing estimation over untrusted networks.
@article{LCSS21_Ristic,
title = {{Secure Fast Covariance Intersection Using Partially Homomorphic and Order Revealing Encryption Schemes}},
author = {Marko Ristic and Benjamin Noack and Uwe D. Hanebeck},
doi = {10.1109/LCSYS.2020.3000649},
issn = {2475-1456},
journal = {IEEE Control Systems Letters},
month = jan,
number = {1},
pages = {217--222},
volume = {5},
year = {2021}
}
Conferences
Haibin Zhao, Christopher Funk, Benjamin Noack, Uwe D. Hanebeck, Michael Beigl
Kalman Filtered Compressive Sensing Using Pseudo-Measurements Proceedings of the 2021 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI 2021), Karlsruhe, Germany, September, 2021.
In this paper, we combine the Kalman filter and compressive sensing using pseudo-measurements in order to reduce the number of measurements usually required by the Kalman filter. To overcome the non-sparsity of the measurement vectors, we make use of the change of their coefficients when represented in a certain basis, reduce the dimensionality of the coefficients, and learn a sparse basis for the measurement vectors. We further improve our proposed method by introducing dynamic weighting of the pseudo-measurements, by aiding compressive measurement reconstruction with Kalman filter estimates and by employing iterative versions of this process. Simulations show that our approach achieves a 37 percent improvement with respect to the mean-square error compared to the traditional Kalman filter with the same number of measurements. Our approach yields better results when the measurement noise is relatively large compared to the system noise, and it significantly improves the accuracy of state estimation in sensor networks with low sensor precision.
@inproceedings{MFI21_Zhao,
title = {{Kalman Filtered Compressive Sensing Using Pseudo-Measurements}},
author = {Haibin Zhao and Christopher Funk and Benjamin Noack and Uwe D. Hanebeck and Michael Beigl},
booktitle = {Proceedings of the 2021 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI 2021)},
address = {Karlsruhe, Germany},
doi = {10.1109/MFI52462.2021.9591186},
month = sep,
year = {2021}
}
2020
Journal Articles
Georg Maier, Florian Pfaff, Andrea Bittner, Robin Gruna, Benjamin Noack, Harald Kruggel-Emden, Uwe D. Hanebeck, Thomas Längle, Jürgen Beyerer
Characterizing Material Flow in Sensor-Based Sorting Systems Using an Instrumented Particle at – Automatisierungstechnik, vol. 4, April, 2020.
Sensor-based sorting is a well-established single particle separation technology. It has found wide application as a quality assurance and control approach in food processing, mining, and recycling. In order to assure high sorting quality, a high degree of control of the motion of individual particles contained in the material stream is required. Several system designs, which are tailored to a sorting task at hand, exist. However, the suitability of a design for a sorting task is assessed by empirical observation. The required thorough experimentation is very time consuming and labor intensive. In this paper, we propose an instrumented bulk material particle for the characterization of motion behavior of the material stream in sensor-based sorting systems. We present a hardware setup including a 9-axis absolute orientation sensor that is used for data acquisition on an experimental sorting system. The presented results show that further processing of this data yields meaningful features of the motion behavior. As an example, we acquire and process data from an experimental sorting system consisting of several submodules such as vibrating conveyor channels and a chute. It is shown that the data can be used to train a model which enables predicting the submodule of a sorting system from which an unknown data sample originates. To our best knowledge, this is the first time that this IIoT-based approach has been applied for the characterization of material flow properties in sensor-based sorting.
@article{AT20_Maier,
title = {{Characterizing Material Flow in Sensor-Based Sorting Systems Using an Instrumented Particle}},
author = {Georg Maier and Florian Pfaff and Andrea Bittner and Robin Gruna and Benjamin Noack and Harald Kruggel-Emden and Uwe D. Hanebeck and Thomas L{\"a}ngle and J{\"u}rgen Beyerer},
doi = {10.1515/auto-2019-0128},
issue = {68},
journal = {at -- Automatisierungstechnik},
month = apr,
volume = {4},
year = {2020}
}
Florian Pfaff, Christoph Pieper, Georg Maier, Benjamin Noack, Robin Gruna, Harald Kruggel-Emden, Uwe D. Hanebeck, Siegmar Wirtz, Viktor Scherer, Thomas Längle, Jürgen Beyerer
Predictive Tracking with Improved Motion Models for Optical Belt Sorting at – Automatisierungstechnik, vol. 4, April, 2020.
Optical belt sorters are a versatile means to sort bulk materials. In previous work, we presented a novel design of an optical belt sorter, which includes an area scan camera instead of a line scan camera. Line scan cameras, which are well-established in optical belt sorting, only allow for a single observation of each particle. Using multitarget tracking, the data of the area scan camera can be used to derive a part of the trajectory of each particle. The knowledge of the trajectories can be used to generate accurate predictions as to when and where each particle passes the separation mechanism. Accurate predictions are key to achieve high quality sorting results. The accuracy of the trajectories and the predictions heavily depends on the motion model used. In an evaluation based on a simulation that provides us with ground truth trajectories, we previously identified a bias in the temporal component of the prediction. In this paper, we analyze the simulation-based ground truth data of the motion of different bulk materials and derive models specifically tailored to the generation of accurate predictions for particles traveling on a conveyor belt. The derived models are evaluated using simulation data involving three different bulk materials. The evaluation shows that the constant velocity model and constant acceleration model can be outperformed by utilizing the similarities in the motion behavior of particles of the same type.
@article{AT20_Pfaff,
title = {{Predictive Tracking with Improved Motion Models for Optical Belt Sorting}},
author = {Florian Pfaff and Christoph Pieper and Georg Maier and Benjamin Noack and Robin Gruna and Harald Kruggel-Emden and Uwe D. Hanebeck and Siegmar Wirtz and Viktor Scherer and Thomas L{\"a}ngle and J{\"u}rgen Beyerer},
doi = {10.1515/auto-2019-0134},
issue = {68},
journal = {at -- Automatisierungstechnik},
month = apr,
volume = {4},
year = {2020}
}
Georg Maier, Florian Pfaff, Christoph Pieper, Robin Gruna, Benjamin Noack, Harald Kruggel-Emden, Thomas Längle, Uwe D. Hanebeck, Jürgen Beyerer
Experimental Evaluation of a Novel Sensor-Based Sorting Approach Featuring Predictive Real-Time Multiobject Tracking IEEE Transactions on Industrial Electronics, February, 2020.
Sensor-based sorting is a machine vision application that has found industrial application in various fields. An accept-or-reject task is executed by separating a material stream into two fractions. Current systems use line-scanning sensors, which is convenient as the material is perceived during transportation. However, line-scanning sensors yield a single observation of each object and no information about their movement. Due to a delay between localization and separation, assumptions regarding the location and point in time for separation need to be made based on the prior localization. Hence, it is necessary to ensure that all objects are transported at uniform velocities. This is often a complex and costly solution. In this paper, we propose a new method for reliably separating particles at non-uniform velocities. The problem is transferred from a mechanical to an algorithmic level. Our novel advanced image processing approach includes equipping the sorter with an area-scan camera in combination with a real-time multiobject tracking system, which enables predictions of the location of individual objects for separation. For the experimental validation of our approach, we present a modular sorting system, which allows comparing sorting results using a line-scan and area-scan camera. Results show that our approach performs reliable separation and hence increases sorting efficiency.
@article{TIE20_Maier,
title = {{Experimental Evaluation of a Novel Sensor-Based Sorting Approach Featuring Predictive Real-Time Multiobject Tracking}},
author = {Georg Maier and Florian Pfaff and Christoph Pieper and Robin Gruna and Benjamin Noack and Harald Kruggel-Emden and Thomas L{\"a}ngle and Uwe D. Hanebeck and J{\"u}rgen Beyerer},
doi = {10.1109/TIE.2020.2970643},
journal = {IEEE Transactions on Industrial Electronics},
month = feb,
url = {https://ieeexplore.ieee.org/document/8984697},
year = {2020}
}
Conferences
Christopher Funk, Benjamin Noack, Uwe D. Hanebeck
Conservative Quantization of Fast Covariance Intersection Proceedings of the 2020 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI 2020), Virtual, September, 2020.
Sensor data fusion in wireless sensor networks poses challenges with respect to both theory and implementation. Unknown cross-correlations between estimates distributed across the network need to be addressed carefully as neglecting them leads to overconfident fusion results. In addition, limited processing power and energy supply of the sensor nodes prohibit the use of complex algorithms and high-bandwidth communication. In this work, fast covariance intersection using both quantized estimates and quantized covariance matrices is considered. The proposed method is computationally efficient and significantly reduces the bandwidth required for data transmission while retaining unbiasedness and conservativeness of fast covariance intersection. The performance of the proposed method is evaluated with respect to that of fast covariance intersection, which proves its effectiveness even in the case of substantial data reduction.
@inproceedings{MFI20_Funk,
title = {{Conservative Quantization of Fast Covariance Intersection}},
author = {Christopher Funk and Benjamin Noack and Uwe D. Hanebeck},
booktitle = {Proceedings of the 2020 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI 2020)},
address = {Virtual},
doi = {10.1109/MFI49285.2020.9235249},
month = sep,
year = {2020}
}
Susanne Radtke, Benjamin Noack, Uwe D. Hanebeck
Fully Decentralized Estimation Using Square-Root Decompositions Proceedings of the 23rd International Conference on Information Fusion (Fusion 2020), Virtual, July, 2020.
Networks consisting of several spatially distributed sensor nodes are useful in many applications. While distributed processing of information can be more robust and flexible than centralized filtering, it requires careful consideration of dependencies between local state estimates.
This paper proposes an algorithm to keep track of dependencies in decentralized systems where no dedicated fusion center is present. Specifically, it addresses double counting of measurement information due to intermediate fusion results as well as correlations due to common process noise and common prior information. To limit the necessary amount of data, this paper introduces a method to bound correlations partially, leading to a more conservative fusion result while reducing the necessary amount of data. Simulation studies compare the performance and convergence rate of the proposed algorithm to other state-of-the-art methods.
@inproceedings{Fusion20_Radtke,
title = {{Fully Decentralized Estimation Using Square-Root Decompositions}},
author = {Susanne Radtke and Benjamin Noack and Uwe D. Hanebeck},
booktitle = {Proceedings of the 23rd International Conference on Information Fusion (Fusion 2020)},
address = {Virtual},
annote = {Winner Best Paper Award},
doi = {10.23919/FUSION45008.2020.9190294},
month = jul,
year = {2020}
}
Kailai Li, Johannes Cox, Benjamin Noack, Uwe D. Hanebeck
Improved Pose Graph Optimization for Planar Motions Using Riemannian Geometry on the Manifold of Dual Quaternions Proceedings of the 21st IFAC World Congress (IFAC 2020), Berlin, Germany, July, 2020.
We present a novel Riemannian approach for planar pose graph optimization problems. By formulating the cost function based on the Riemannian metric on the manifold of dual quaternions representing planar motions, the nonlinear structure of the SE(2) group is inherently considered. To solve the on-manifold least squares problem, a Riemannian Gauss--Newton method using the exponential retraction is applied. The proposed Riemannian pose graph optimizer (RPG-Opt) is further evaluated based on public planar pose graph data sets. Compared with state-of-the-art frameworks, the proposed method gives equivalent accuracy and better convergence robustness under large uncertainties of odometry measurements.
@inproceedings{IFAC20_Li-PoseGraph,
title = {{Improved Pose Graph Optimization for Planar Motions Using Riemannian Geometry on the Manifold of Dual Quaternions}},
author = {Kailai Li and Johannes Cox and Benjamin Noack and Uwe D. Hanebeck},
booktitle = {Proceedings of the 21st IFAC World Congress (IFAC 2020)},
address = {Berlin, Germany},
doi = {10.1016/j.ifacol.2020.12.2432},
month = jul,
year = {2020}
}
Benjamin Noack, Christopher Funk, Susanne Radtke, Uwe D. Hanebeck
State Estimation with Event-Based Inputs Using Stochastic Triggers Proceedings of the 21st IFAC World Congress (IFAC 2020), Berlin, Germany, July, 2020.
Event-based communication and state estimation offer the potential to improve resource utilization in networked sensor and control systems significantly. Sensor nodes can trigger transmissions when data are deemed useful for the remote estimation units. To improve the estimation performance, the remote estimator can exploit the implicit information conveyed by the event trigger even if no transmission is triggered. The implicit information is typically incorporated into the measurement update of a remote Kalman filter. In this paper, event-triggered transmissions of input data are investigated that enter the prediction step of the remote estimator.
By employing a stochastic trigger, the implicit input information
remains Gaussian and can easily be incorporated into the remote Kalman filter. The proposed event-based scheme is evaluated in remote tracking scenarios, where system inputs are transmitted aperiodically.
@inproceedings{IFAC20_Noack,
title = {{State Estimation with Event-Based Inputs Using Stochastic Triggers}},
author = {Benjamin Noack and Christopher Funk and Susanne Radtke and Uwe D. Hanebeck},
booktitle = {Proceedings of the 21st IFAC World Congress (IFAC 2020)},
address = {Berlin, Germany},
doi = {10.1016/j.ifacol.2020.12.2491},
month = jul,
year = {2020}
}
Susanne Radtke, Benjamin Noack, Uwe D. Hanebeck
Reconstruction of Cross-Correlations between Heterogeneous Trackers Using Deterministic Samples Proceedings of the 21st IFAC World Congress (IFAC 2020), Berlin, Germany, July, 2020.
The exploitation of dependencies between state estimates from distributed trackers plays a vital role in so-called track-to-track fusion and has been extensively studied for state estimates with the same state space. In contrast, dependencies are often neglected when considering heterogeneous state estimates referring to different state spaces, since the necessary transformations make the analytic calculation complex or infeasible. This paper aims to develop an overarching framework for the reconstruction of cross-covariances between state estimates obtained in heterogeneous state spaces. The proposed method uses a set of deterministic samples to calculate dependent information. Thus, it allows for a distributed track-keeping of correlations that also encodes the transformation into the local subsystems. To highlight the algorithm, weuse a linear problem with heterogeneous trackers only and discuss the correlation problem in detail. The results show superior performance compared to neglecting the correlations.
@inproceedings{IFAC20_Radtke,
title = {{Reconstruction of Cross-Correlations between Heterogeneous Trackers Using Deterministic Samples}},
author = {Susanne Radtke and Benjamin Noack and Uwe D. Hanebeck},
booktitle = {Proceedings of the 21st IFAC World Congress (IFAC 2020)},
address = {Berlin, Germany},
doi = {10.1016/j.ifacol.2020.12.1122},
month = jul,
year = {2020}
}
2019
Journal Articles
Eva Julia Schmitt, Benjamin Noack, Wolfgang Krippner, Uwe D. Hanebeck
Gaussianity-Preserving Event-Based State Estimation with an FIR-Based Stochastic Trigger IEEE Control Systems Letters, vol. 3, no. 3, pp. 769–774, July, 2019.
With modern communication technology, sensors, estimators, and controllers can be pushed apart to distribute
intelligence over wide distances. Instead of congesting channels by periodic data transmissions, smart sensors can decide
on their own whether data are worth transmitting. This paper studies event-based transmissions from sensor to estimator.
The sensor-side event trigger conveys usable information even if no transmission is triggered. In the absence of data,
such implicit information can still be exploited by the remote Kalman filter. For this purpose, an easy-to-implement
triggering mechanism is proposed based on a Finite Impulse Response prediction that is compared against a stochastic
decision variable. By the aid of the stochastic event trigger, the implicit information retains a Gaussian representation
and can easily be processed by the Kalman filter. The parameters for the stochastic trigger are retrieved from the
Finite Impulse Response filter, which contributes to reducing the communication rate significantly, as shown in simulations.
@article{LCSS19_Schmitt,
title = {{Gaussianity-Preserving Event-Based State Estimation with an FIR-Based Stochastic Trigger}},
author = {Eva Julia Schmitt and Benjamin Noack and Wolfgang Krippner and Uwe D. Hanebeck},
doi = {10.1109/LCSYS.2019.2918024},
issn = {2475-1456},
journal = {IEEE Control Systems Letters},
month = jul,
number = {3},
pages = {769--774},
volume = {3},
year = {2019}
}
Conferences
Benjamin Noack, Umut Orguner, Uwe D. Hanebeck
Nonlinear Decentralized Data Fusion with Generalized Inverse Covariance Intersection Proceedings of the 22nd International Conference on Information Fusion (Fusion 2019), Ottawa, Canada, July, 2019.
Decentralized data fusion is a challenging task even for linear estimation problems. Nonlinear estimation renders data fusion even more difficult as dependencies among the nonlinear estimates require complicated parameterizations. It is nearly impossible to reconstruct or keep track of dependencies. Therefore, conservative approaches have become a popular solution to nonlinear data fusion. As a generalization of Covariance Intersection, exponential mixture densities have been widely applied for nonlinear fusion. However, this approach inherits the conservativeness of Covariance Intersection. For this reason, the less conservative fusion rule Inverse Covariance Intersection is studied in this paper and also generalized to nonlinear data fusion. This generalization employs a conservative approximation of the common information shared by the estimates to be fused. This bound of the common information is subtracted from the fusion result. In doing so, less conservative fusion results can be attained as an empirical analysis demonstrates.
@inproceedings{Fusion19_Noack,
title = {{Nonlinear Decentralized Data Fusion with Generalized Inverse Covariance Intersection}},
author = {Benjamin Noack and Umut Orguner and Uwe D. Hanebeck},
booktitle = {Proceedings of the 22nd International Conference on Information Fusion (Fusion 2019)},
address = {Ottawa, Canada},
doi = {10.23919/FUSION43075.2019.9011163},
month = jul,
url = {https://ieeexplore.ieee.org/document/9011163},
year = {2019}
}
Susanne Radtke, Benjamin Noack, Uwe D. Hanebeck
Distributed Estimation using Square Root Decompositions of Dependent Information Proceedings of the 22nd International Conference on Information Fusion (Fusion 2019), Ottawa, Canada, July, 2019.
Sensor networks allow robust and precise estimation by fusing estimates from several distributed sensor nodes. Because of the often limited communication resources, a trade-off between the amount of information communicated and the quality of the fusion result has to be made. On the one hand, obtaining the optimal fusion result often needs an infeasible amount of additional information, but on the other hand, conservative methods usually lead to more pessimistic results in comparison. This paper proposes a square root decomposition of the incorporated noise terms to reconstruct the cross-covariance matrices between sensor nodes. To save communication bandwidth, a residual is defined that allows bounding of the cross-covariance matrix with a reduced number of noise terms. The consistency of the proposed method is demonstrated by two simulation examples featuring a linear and a nonlinear setup and is compared with other state-of-the-art fusion methods.
@inproceedings{Fusion19_Radtke,
title = {{Distributed Estimation using Square Root Decompositions of Dependent Information}},
author = {Susanne Radtke and Benjamin Noack and Uwe D. Hanebeck},
booktitle = {Proceedings of the 22nd International Conference on Information Fusion (Fusion 2019)},
address = {Ottawa, Canada},
doi = {10.23919/FUSION43075.2019.9011162},
month = jul,
url = {https://ieeexplore.ieee.org/document/9011162},
year = {2019}
}
Tobias Kronauer, Florian Pfaff, Benjamin Noack, Wei Tian, Georg Maier, Uwe D. Hanebeck
Feature-Aided Multitarget Tracking for Optical Belt Sorters Proceedings of the 22nd International Conference on Information Fusion (Fusion 2019), Ottawa, Canada, July, 2019.
Industrial optical belt sorters are highly versatile in sorting bulk material or food, especially if mechanical properties are not sufficient for an adequate sorting quality. In previous works, we could show that the sorting quality can be enhanced by replacing the line scan camera, which is normally used, with an area scan camera. By performing multitarget tracking within the field of view, the precision of the utilized separation mechanism can be enhanced. The employed kinematics-based multitarget tracking crucially depends on the ability to associate detection hypotheses of the same particle across multiple frames. In this work, we propose a procedure to incorporate the visual similarity of the detected particles into the kinematics-based multitarget tracking that is generic and evaluates the visual similarity independent of the kinematics. For evaluating the visual similarity, we use the Kernelized Correlation Filter, the Large Margin Nearest Neighbor method and the Normalized Cross Correlation. Although no clear superiority for any of the visual similarity measures mentioned above could be determined, an improvement of all considered error metrics was attained.
@inproceedings{Fusion19_Kronauer,
title = {{Feature-Aided Multitarget Tracking for Optical Belt Sorters}},
author = {Tobias Kronauer and Florian Pfaff and Benjamin Noack and Wei Tian and Georg Maier and Uwe D. Hanebeck},
booktitle = {Proceedings of the 22nd International Conference on Information Fusion (Fusion 2019)},
address = {Ottawa, Canada},
doi = {10.23919/FUSION43075.2019.9011447},
month = jul,
url = {https://ieeexplore.ieee.org/document/9011447},
year = {2019}
}
Susanne Radtke, Benjamin Noack, Uwe D. Hanebeck
Distributed Estimation with Partially Overlapping States based on Deterministic Sample-based Fusion Proceedings of the 2019 European Control Conference (ECC 2019), Naples, Italy, June, 2019.
Distributing workload between sensor nodes is a
practical solution to monitor large-scale phenomena. In doing
so, the system can be split into smaller subsystems that can
be estimated and controlled more easily. While current state-of-
the-art fusion methods for distributed estimation assume the
fusion of estimates referring to the full dimension of the state,
little effort has been made to account for the fusion of unequal
state vectors referring to smaller subsystems of the full system.
In this paper, a novel method to fuse overlapping state vectors
using a deterministic sample-based fusion method is proposed.
These deterministic samples can be used to account for the
correlated and uncorrelated noise terms and are therefore able
to reconstruct the joint covariance matrix in a distributed
fashion. The performance of the proposed fusion method is
compared to other state-of-the-art methods.
@inproceedings{ECC19_Radtke,
title = {{Distributed Estimation with Partially Overlapping States based on Deterministic Sample-based Fusion}},
author = {Susanne Radtke and Benjamin Noack and Uwe D. Hanebeck},
booktitle = {Proceedings of the 2019 European Control Conference (ECC 2019)},
address = {Naples, Italy},
doi = {10.23919/ECC.2019.8795853},
month = jun,
year = {2019}
}
Kailai Li, Daniel Frisch, Benjamin Noack, Uwe Hanebeck
Geometry-Driven Deterministic Sampling for Nonlinear Bingham Filtering Proceedings of the 2019 European Control Conference (ECC 2019), Naples, Italy, June, 2019.
We propose a geometry-driven deterministic sampling
method for Bingham distributions in arbitrary dimensions.
With flexibly adjustable sampling sizes, the novel scheme
can generate equally weighted samples that satisfy requirements
of the unscented transform and approximate higher-order
shape information of the Bingham distribution. By leveraging
retraction techniques from Riemannian geometry, the sigma
points are constrained to preserve the second-order moment.
Meanwhile, samples in each principal direction are located in a
way that minimizes a distance measure between the on-tangentplane
Dirac mixtures and the underlying on-manifold density.
For that, the modified Cram´er–von Mises distance based on
the localized cumulative distribution (LCD) is employed. We
further integrate the proposed approach into a quaternionbased
orientation estimation framework. Compared to the
existing unscented sampling approach drawing only fixed and
limited numbers of sigma points, simulation results show that
the proposed scheme enables better accuracy and robustness
for nonlinear Bingham filtering.
@inproceedings{ECC19_Li,
title = {{Geometry-Driven Deterministic Sampling for Nonlinear Bingham Filtering}},
author = {Kailai Li and Daniel Frisch and Benjamin Noack and Uwe Hanebeck},
booktitle = {Proceedings of the 2019 European Control Conference (ECC 2019)},
address = {Naples, Italy},
doi = {10.23919/ECC.2019.8796102},
month = jun,
year = {2019}
}
Selim Özgen, Saskia Kohn, Benjamin Noack, Uwe D. Hanebeck
State Estimation with Model-Mismatch-Based Secrecy against Eavesdroppers Proceedings of the 2019 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI 2019), Taipei, Taiwan, May, 2019.
This study takes into consideration remote state estimation, where the state of a system is to be shared with a number of authorized users for any purpose (e.g., tracking, control), in the presence of eavesdroppers. We propose a novel control-theoretic secrecy mechanism to securely transmit the state estimate among the authorized users in the system. Moreover, as there isn't any cryptographic mechanism applied to the shared information in the conventional sense, it is not possible for the eavesdroppers to understand that the state estimate is hidden. A use-case of the proposed secrecy mechanism for a target tracking example is also demonstrated.
@inproceedings{MFI19_Oezgen,
title = {{State Estimation with Model-Mismatch-Based Secrecy against Eavesdroppers}},
author = {Selim {\"O}zgen and Saskia Kohn and Benjamin Noack and Uwe D. Hanebeck},
booktitle = {Proceedings of the 2019 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI 2019)},
address = {Taipei, Taiwan},
doi = {10.1109/ICPHYS.2019.8780166},
month = may,
year = {2019}
}
Susanne Radtke, Kailai Li, Benjamin Noack, Uwe D. Hanebeck
Comparative Study of Track-to-Track Fusion Methods for Cooperative Tracking with Bearings-only Measurements Proceedings of the 2019 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI 2019), Taipei, Taiwan, May, 2019.
Using a network of spatially distributed sensors to track a moving object can be a challenging task.
In applications with limited communication between sensor nodes and packet loss, it may be impossible to process
measurements from these distributed sensor nodes in a central unit. Therefore, it is often necessary to use only
the locally available measurements at the sensor nodes and afterwards merge all local tracks into one consistent result.
In this paper, several different track-to-track fusion algorithms are compared to cooperatively track a moving object
using only bearing measurements. It is shown that the Sample-based Fusion that uses a set of deterministic samples to
reconstruct the cross-covariances is a suitable fusion algorithm for the considered setup. Furthermore, it provides
the means to efficiently keep track of the cross-covariances between sensor nodes and therefore outperforms
conservative methods. The proposed approach is also tested in a real-world indoor localization setup using
bearings-only acoustic measurements from three microphone arrays.
@inproceedings{MFI19_Radtke,
title = {{Comparative Study of Track-to-Track Fusion Methods for Cooperative Tracking with Bearings-only Measurements}},
author = {Susanne Radtke and Kailai Li and Benjamin Noack and Uwe D. Hanebeck},
booktitle = {Proceedings of the 2019 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI 2019)},
address = {Taipei, Taiwan},
doi = {10.1109/ICPHYS.2019.8780330},
month = may,
year = {2019}
}
2018
Book Chapters
Florian Rosenthal, Benjamin Noack, Uwe D. Hanebeck
State Estimation in Networked Control Systems with Delayed and Lossy Acknowledgments Multisensor Fusion and Integration in the Wake of Big Data, Deep Learning and Cyber Physical System, pp. 22–38, Springer International Publishing, Cham, July, 2018.
In this article, we are concerned with state estimation in Networked Control Systems where both control inputs and measurements are transmitted over networks which are lossy and introduce random transmission delays. We focus on the case where acknowledgment packets transmitted by the actuator upon reception of applicable control inputs are also subject to delays and losses, as opposed to the common notion of TCP-like communication where successful transmissions are acknowledged instantaneously and without losses. As a consequence, the state estimator in the considered setup has only partial and belated knowledge concerning the actually applied control inputs which results in additional uncertainty. We derive an estimator by extending an existing approach for the special case of UDP-like communication which maintains estimates of the applied control inputs that are incorporated into the estimation of the plant state. The presented estimator is compared to the original approach in terms of Monte Carlo simulations where its increased robustness towards imperfect knowledge of the underlying networks is indicated.
@incollection{LNEE18_Rosenthal,
title = {{State Estimation in Networked Control Systems with Delayed and Lossy Acknowledgments}},
author = {Florian Rosenthal and Benjamin Noack and Uwe D. Hanebeck},
booktitle = {Multisensor Fusion and Integration in the Wake of Big Data, Deep Learning and Cyber Physical System},
address = {Cham},
doi = {10.1007/978-3-319-90509-9_2},
editor = {Sukhan Lee and Hanseok Ko and Songhwai Oh},
isbn = {978-3-319-90509-9},
month = jul,
pages = {22--38},
publisher = {Springer International Publishing},
url = {https://link.springer.com/chapter/10.1007/978-3-319-90509-9_2},
year = {2018}
}
Journal Articles
Christoph Pieper, Florian Pfaff, Georg Maier, Harald Kruggel-Emden, Siegmar Wirtz, Benjamin Noack, Robin Gruna, Viktor Scherer, Uwe D. Hanebeck, Thomas Längle, Jürgen Beyerer
Numerical Modelling of an Optical Belt Sorter Using a DEM–CFD Approach Coupled with Particle Tracking and Comparison with Experiments Powder Technology, vol. 370, pp. 181–193, December, 2018.
State-of-the-art optical sorting systems suffer from delays between the particle detection and separation stage, during which the material movement is not accounted for. Commonly line scan cameras, using simple assumptions to predict the future particle movement, are employed. In this study, a novel prediction approach is presented, where an area scan camera records the particle movement over multiple time steps and a tracking algorithm is used to reconstruct the corresponding paths to determine the time and position at which the material reaches the separation stage. In order to assess the benefit of such a model at different operating parameters, an automated optical belt sorter is numerically modelled and coupled with the tracking procedure. The Discrete Element Method (DEM) is used to describe the particle–particle as well as particle–wall interactions, while the air nozzles required for deflecting undesired material fractions are described with Computational Fluid Dynamics (CFD). The accuracy of the employed numerical approach is ensured by comparing the separation results of a predefined sorting task with experimental investigations. The quality of the aforementioned prediction models is compared when utilizing different belt lengths, nozzle activation durations, particle types, sampling frequencies and detection windows. Results show that the numerical model of the optical belt sorter is able to accurately describe the sorting system and is suitable for detailed investigation of various operational parameters. The proposed tracking prediction model was found to be superior to the common line scan camera method in all investigated scenarios. Its advantage is especially profound when difficult sorting conditions, e.g. short conveyor belt lengths or uncooperative moving bulk solids, apply.
@article{PowTec18_Pieper,
title = {{Numerical Modelling of an Optical Belt Sorter Using a DEM\textendash CFD Approach Coupled with Particle Tracking and Comparison with Experiments}},
author = {Christoph Pieper and Florian Pfaff and Georg Maier and Harald Kruggel-Emden and Siegmar Wirtz and Benjamin Noack and Robin Gruna and Viktor Scherer and Uwe D. Hanebeck and Thomas L{\"a}ngle and J{\"u}rgen Beyerer},
doi = {10.1016/j.powtec.2018.09.003},
journal = {Powder Technology},
month = dec,
pages = {181--193},
volume = {370},
year = {2018}
}
Jindřich Duník, Ondřej Straka, Benjamin Noack, Jannik Steinbring, Uwe D. Hanebeck
On Directional Splitting of Gaussian Density in Nonlinear Random Variable Transformation IET Signal Processing, July, 2018.
Transformation of a random variable is a common need in a design of many algorithms in signal processing, automatic
control, and fault detection. Typically, the design is tied to an assumption on a probability density function of the random variable,
often in the form of the Gaussian distribution. The assumption may be, however, difficult to be met in algorithms involving nonlinear
transformation of the random variable. This paper focuses on techniques capable to ensure validity of the Gaussian assumption of
the nonlinearly transformed Gaussian variable by approximating the to-be-transformed random variable distribution by a Gaussian
mixture distribution. The stress is laid on an analysis and selection of design parameters of the approximate Gaussian mixture
distribution to minimise the error imposed by the nonlinear transformation such as the location and number of the Gaussian mixture
terms. A special attention is devoted to the definition of the novel Gaussian mixture splitting directions based on the measures of
non-Gaussianity. The proposed splitting directions are analysed and illustrated in numerical simulations.
@article{IETSP2018_Dunik,
title = {{On Directional Splitting of Gaussian Density in Nonlinear Random Variable Transformation}},
author = {Jind{\v r}ich Dun{\'\i}k and Ond{\v r}ej Straka and Benjamin Noack and Jannik Steinbring and Uwe D. Hanebeck},
doi = {10.1049/iet-spr.2017.0286},
issn = {1751-9683},
journal = {IET Signal Processing},
month = jul,
url = {http://digital-library.theiet.org/content/journals/10.1049/iet-spr.2017.0286},
year = {2018}
}
Katharina Dormann, Benjamin Noack, Uwe D. Hanebeck
Optimally Distributed Kalman Filtering with Data-Driven Communication Sensors, vol. 18, no. 4, April, 2018.
For multisensor data fusion, distributed state estimation techniques that enable a local processing of sensor data are the means of choice in order to minimize storage and communication costs. In particular, a distributed implementation of the optimal Kalman filter has recently been developed. A significant disadvantage of this algorithm is that the fusion center needs access to each node so as to compute a consistent state estimate, which requires full communication each time an estimate is requested. In this article, different extensions of the optimally distributed Kalman filter are proposed that employ data-driven transmission schemes in order to reduce communication expenses. As a first relaxation of the full-rate communication scheme, it can be shown that each node only has to transmit every second time step without endangering consistency of the fusion result. Also, two data-driven algorithms are introduced that even allow for lower transmission rates, and bounds are derived to guarantee consistent fusion results. Simulations demonstrate that the data-driven distributed filtering schemes can outperform a centralized Kalman filter that requires each measurement to be sent to the center node.
@article{Sensors18_Dormann,
title = {{Optimally Distributed Kalman Filtering with Data-Driven Communication}},
author = {Katharina Dormann and Benjamin Noack and Uwe D. Hanebeck},
doi = {10.3390/s18041034},
issn = {1424-8220},
journal = {Sensors},
month = apr,
number = {4},
url = {http://www.mdpi.com/1424-8220/18/4/1034},
volume = {18},
year = {2018}
}
Conferences
Kailai Li, Daniel Frisch, Susanne Radtke, Benjamin Noack, Uwe D. Hanebeck
Wavefront Orientation Estimation Based on Progressive Bingham Filtering Proceedings of the IEEE ISIF Workshop on Sensor Data Fusion: Trends, Solutions, Applications (SDF 2018), October, 2018.
In this paper, we propose the Progressive Bingham
Filter (PBF), a novel stochastic filtering algorithm for nonlinear
spatial orientation estimation. As an extension of the orientation
filter previously proposed only for the identity measurement
model based on the Bingham distribution, our method is able to
handle arbitrary measurement models. Instead of the sampling-
approximation scheme used in the prediction step, a closed-
form solution is possible when the system equation is based on
the Hamilton product. Besides stochastic approaches, we also
introduce the Spherical Averaging Method (SAM), which is an
application of the Riemannian averaging technique. The two
approaches are then applied to a specific problem where the
wavefront orientation is estimated based on Time Differences of
Arrival (TDOA) and evaluated in simulations. The results show
theoretical competitiveness of the PBF.
@inproceedings{SDF18_Li,
title = {{Wavefront Orientation Estimation Based on Progressive Bingham Filtering}},
author = {Kailai Li and Daniel Frisch and Susanne Radtke and Benjamin Noack and Uwe D. Hanebeck},
booktitle = {Proceedings of the IEEE ISIF Workshop on Sensor Data Fusion: Trends, Solutions, Applications (SDF 2018)},
doi = {10.1109/SDF.2018.8547094},
month = oct,
year = {2018}
}
Susanne Radtke, Benjamin Noack, Uwe D. Hanebeck, Ondřej Straka
Reconstruction of Cross-Correlations with Constant Number of Deterministic Samples Proceedings of the 21st International Conference on Information Fusion (Fusion 2018), Cambridge, United Kingdom, July, 2018.
Optimal fusion of estimates that are computed in a distributed fashion is a challenging task. In general, the sensor nodes cannot keep track of the cross-correlations required to fuse estimates optimally. In this paper, a novel technique is presented that provides the means to reconstruct the required correlation structure. For this purpose, each node computes a set of deterministic samples that provides all the information required to reassemble the cross-covariance matrix for each pair of estimates. As the number of samples is increasing over time, a method to reduce the size of the sample set is presented and studied. In doing so, communication expenses can be reduced significantly, but approximation errors are possibly introduced by neglecting past correlation terms. In order to keep approximation errors at a minimum, an appropriate set size can be determined and a trade-off between communication expenses and estimation quality can be found.
@inproceedings{Fusion18_Radtke,
title = {{Reconstruction of Cross-Correlations with Constant Number of Deterministic Samples}},
author = {Susanne Radtke and Benjamin Noack and Uwe D. Hanebeck and Ond{\v r}ej Straka},
booktitle = {Proceedings of the 21st International Conference on Information Fusion (Fusion 2018)},
address = {Cambridge, United Kingdom},
doi = {10.23919/ICIF.2018.8455221},
month = jul,
url = {https://ieeexplore.ieee.org/document/8455221},
year = {2018}
}
Selim Özgen, Uwe D. Hanebeck, Benjamin Noack, Marco Huber, Florian Rosenthal, Jana Mayer
Retrodiction of Data Association Probabilities via Convex Optimization Proceedings of the 21st International Conference on Information Fusion (Fusion 2018), Cambridge, United Kingdom, July, 2018.
In a surveillance environment with high clutter,
finding the correct measurement to track associations becomes
extremely important for efficient target tracking. This study
offers a novel algorithm to retrodict the data association probabilities
at any past time instant, when the batch set of measurements
is kept in memory. For the retrodiction procedure, the batch
association cost is first written explicitly as a binary integer
optimization problem with a quadratic cost function and it is
shown that the relaxed form of the problem is convex. From the
relaxed problem, a lower bound for the optimal association cost
is derived, and this lower bound is used as the data association
probabilities pertaining to that selected time instant in the past.
Due to its consideration of the batch set of data in a retrospective
manner, we will call this algorithm as Retrodictive Probabilistic
Data Association, RPDA. For simplification of the mathematical
analysis, a single point target with no missing measurements, i.e.,
PD = 1, is taken into account.
@inproceedings{FUSION18_Oezgen,
title = {{Retrodiction of Data Association Probabilities via Convex Optimization}},
author = {Selim {\"O}zgen and Uwe D. Hanebeck and Benjamin Noack and Marco Huber and Florian Rosenthal and Jana Mayer},
booktitle = {Proceedings of the 21st International Conference on Information Fusion (Fusion 2018)},
address = {Cambridge, United Kingdom},
doi = {10.23919/ICIF.2018.8455857},
month = jul,
year = {2018}
}
Mikhail Aristov, Benjamin Noack, Uwe D. Hanebeck, Jörn Müller-Quade
Encrypted Multisensor Information Filtering Proceedings of the 21st International Conference on Information Fusion (Fusion 2018), Cambridge, United Kingdom, July, 2018.
With the advent of cheap sensor technology, multisensor data fusion algorithms have been becoming a key enabler for efficient in-network processing of sensor data. The information filter, in particular, has proven useful due to its simple additive structure of the measurement update equations.
In order to exploit this structure for an efficient in-network processing, each node in the network is supposed to locally process and combine data from its neighboring nodes. The aspired in-network processing, at first glance, prohibits efficient privacy-preserving communication protocols, and encryption schemes that allow for algebraic manipulations are often computationally too expensive. Partially homomorphic encryption schemes constitute far more practical solutions but are restricted to a single algebraic operation on the corresponding ciphertexts. In this paper, an additive-homomorphic encryption scheme is used to derive a privacy-preserving implementation of the information filter where additive operations are sufficient to distribute the workload among the sensor nodes. However, the encryption scheme requires the floating-point data to be quantized, which impairs the estimation quality. The proposed filter and the implications of the necessary quantization are analyzed in a simulated multisensor tracking scenario.
@inproceedings{Fusion18_Aristov,
title = {{Encrypted Multisensor Information Filtering}},
author = {Mikhail Aristov and Benjamin Noack and Uwe D. Hanebeck and J{\"o}rn M{\"u}ller-Quade},
booktitle = {Proceedings of the 21st International Conference on Information Fusion (Fusion 2018)},
address = {Cambridge, United Kingdom},
doi = {10.23919/ICIF.2018.8455449},
month = jul,
year = {2018}
}
Florian Rosenthal, Benjamin Noack, Uwe D. Hanebeck
Scheduling of Measurement Transmission in Networked Control Systems Subject to Communication Constraints Proceedings of the 2018 American Control Conference (ACC 2018), Milwaukee, Wisconsin, USA, June, 2018.
In this paper, we consider Networked Control Systems where the transmission of sensor data is restricted in terms of a fixed communication budget due to the limited capacity of the underlying network. Therefore, the remote estimator cannot be supplied with measurements every time step, which impacts the accuracy of the estimates and consequently the achievable control performance. In order to trade off estimation accuracy against the costs of measurement transmission, we formulate the considered task as an optimal control problem, so that it fits into the broader class of sensor and measurement scheduling problems. As the optimal solution of such problems is generally intractable, we derive a suboptimal algorithm based on randomized rounding. In two numerical examples, we show that the proposed approach can outperfom a state-of-the-art sensor selection algorithm.
@inproceedings{ACC18_Rosenthal,
title = {{Scheduling of Measurement Transmission in Networked Control Systems Subject to Communication Constraints}},
author = {Florian Rosenthal and Benjamin Noack and Uwe D. Hanebeck},
booktitle = {Proceedings of the 2018 American Control Conference (ACC 2018)},
address = {Milwaukee, Wisconsin, USA},
doi = {10.23919/ACC.2018.8431107},
month = jun,
year = {2018}
}
Georg Maier, Florian Pfaff, Christoph Pieper, Robin Gruna, Benjamin Noack, Harald Kruggel-Emden, Thomas Längle, Uwe D. Hanebeck, Siegmar Wirtz, Viktor Scherer, Jürgen Beyerer
Application of Area-Scan Sensors in Sensor-Based Sorting Proceedings of the Eighth Conference on Sensor-Based Sorting & Control 2018 (SBSC 2018), Aachen, Germany, March, 2018.
abstract
BibTeX
In the field of machine vision, sensor-based sorting is an important real-time application that enables the separation of a material feed into different classes. While state-of-the-art systems utilize scanning sensors such as line-scan cameras, advances in sensor technology have made application of area scanning sensors feasible. Provided a sufficiently high frame rate, objects can be observed at multiple points in time. By applying multiobject tracking, information about the objects contained in the material stream can be fused over time. Based on this information, our approach further allows predicting the position of each object for future points in time. While conventional systems typically apply a global, rather simple motion model, our approach includes an individual motion model for each object, which in turn allows estimating the point in time as well as the position when reaching the separation stage. In this contribution, we present results from our collaborative research project and summarize the present advances by discussing the potential of the application of area-scan sensors for sensor-based sorting. Among others, we introduce our simulation-driven approach and present results for physical separation efficiency for simulation-generated data, demonstrate the potential of using motion-based features for material classification and discuss real-time related challenges.
@inproceedings{SBSC18_Maier,
title = {{Application of Area-Scan Sensors in Sensor-Based Sorting}},
author = {Georg Maier and Florian Pfaff and Christoph Pieper and Robin Gruna and Benjamin Noack and Harald Kruggel-Emden and Thomas L{\"a}ngle and Uwe D. Hanebeck and Siegmar Wirtz and Viktor Scherer and J{\"u}rgen Beyerer},
booktitle = {Proceedings of the Eighth Conference on Sensor-Based Sorting \& Control 2018 (SBSC 2018)},
address = {Aachen, Germany},
month = mar,
year = {2018}
}
2017
Journal Articles
Georg Maier, Florian Pfaff, Matthias Wagner, Christoph Pieper, Robin Gruna, Benjamin Noack, Harald Kruggel-Emden, Thomas Längle, Uwe D. Hanebeck, Siegmar Wirtz, Viktor Scherer, Jürgen Beyerer
Real-Time Multitarget Tracking for Sensor-Based Sorting Journal of Real-Time Image Processing, November, 2017.
Utilizing parallel algorithms is an established way of increasing performance in systems that are bound to real-time restrictions. Sensor-based sorting is a machine vision application for which firm real-time requirements need to be respected in order to reliably remove potentially harmful entities from a material feed. Recently, employing a predictive tracking approach using multitarget tracking in order to decrease the error in the physical separation in optical sorting has been proposed. For implementations that use hard associations between measurements and tracks, a linear assignment problem has to be solved for each frame recorded by a camera. The auction algorithm can be utilized for this purpose, which also has the advantage of being well suited for parallel architectures. In this paper, an improved implementation of this algorithm for a graphics processing unit (GPU) is presented. The resulting algorithm is implemented in both an OpenCL and a CUDA based environment. By using an optimized data structure, the presented algorithm outperforms recently proposed implementations in terms of speed while retaining the quality of output of the algorithm. Furthermore, memory requirements are significantly decreased, which is important for embedded systems. Experimental results are provided for two different GPUs and six datasets. It is shown that the proposed approach is of particular interest for applications dealing with comparatively large problem sizes.
@article{RTIP17_Maier,
title = {{Real-Time Multitarget Tracking for Sensor-Based Sorting}},
author = {Georg Maier and Florian Pfaff and Matthias Wagner and Christoph Pieper and Robin Gruna and Benjamin Noack and Harald Kruggel-Emden and Thomas L{\"a}ngle and Uwe D. Hanebeck and Siegmar Wirtz and Viktor Scherer and J{\"u}rgen Beyerer},
doi = {10.1007/s11554-017-0735-y},
journal = {Journal of Real-Time Image Processing},
month = nov,
year = {2017}
}
Georg Maier, Florian Pfaff, Florian Becker, Christoph Pieper, Robin Gruna, Benjamin Noack, Harald Kruggel-Emden, Thomas Längle, Uwe D. Hanebeck, Siegmar Wirtz, Viktor Scherer, Jürgen Beyerer
Motion-Based Material Characterization in Sensor-Based Sorting tm - Technisches Messen, De Gruyter, October, 2017.
Sensor-based sorting provides state-of-the-art solutions for sorting cohesive, granular materials. Typically, involved sensors, illumination, implementation of data analysis and other components are designed and chosen according to the sorting task at hand. A common property of conventional systems is the utilization of scanning sensors. However, the usage of area-scan cameras has recently been proposed. When observing objects at multiple time points, the corresponding paths can be reconstructed by using multiobject tracking. This in turn allows to accurately estimate the point in time and position at which any object will reach the separation stage of the optical sorter and hence contributes to decreasing the error in physical separation. In this paper, it is proposed to further exploit motion information for the purpose of material characterization. By deriving suitable features from the motion information, we show that high classification performance is obtained for an exemplary classification task. The approach therefore contributes towards decreasing the detection error of sorting systems.
@article{TM17_Maier,
title = {{Motion-Based Material Characterization in Sensor-Based Sorting}},
author = {Georg Maier and Florian Pfaff and Florian Becker and Christoph Pieper and Robin Gruna and Benjamin Noack and Harald Kruggel-Emden and Thomas L{\"a}ngle and Uwe D. Hanebeck and Siegmar Wirtz and Viktor Scherer and J{\"u}rgen Beyerer},
doi = {10.1515/teme-2017-0063},
journal = {tm - Technisches Messen, De Gruyter},
month = oct,
year = {2017}
}
Florian Pfaff, Georg Maier, Mikhail Aristov, Benjamin Noack, Robin Gruna, Uwe D. Hanebeck, Thomas Längle, Jürgen Beyerer, Christoph Pieper, Harald Kruggel-Emden, Siegmar Wirtz, Viktor Scherer
Real-Time Motion Prediction Using the Chromatic Offset of Line Scan Cameras at - Automatisierungstechnik, De Gruyter, June, 2017.
State-of-the-art optical belt sorters commonly employ line scan cameras and use simple assumptions to predict each particle's movement, which is required for the separation process. Previously, we have equipped an experimental optical belt sorter with an area scan camera and were able to show that tracking the particles of the bulk material results in an improvement of the predictions and thus also the sorting process. In this paper, we use the slight gap between the sensor lines of an RGB line scan camera to derive information about the particles' movements in real-time. This approach allows improving the predictions in optical belt sorters without necessitating any hardware modifications.
@article{AT17_Pfaff,
title = {{Real-Time Motion Prediction Using the Chromatic Offset of Line Scan Cameras}},
author = {Florian Pfaff and Georg Maier and Mikhail Aristov and Benjamin Noack and Robin Gruna and Uwe D. Hanebeck and Thomas L{\"a}ngle and J{\"u}rgen Beyerer and Christoph Pieper and Harald Kruggel-Emden and Siegmar Wirtz and Viktor Scherer},
doi = {10.1515/auto-2017-0009},
journal = {at - Automatisierungstechnik, De Gruyter},
month = jun,
year = {2017}
}
Benjamin Noack, Joris Sijs, Marc Reinhardt, Uwe D. Hanebeck
Decentralized Data Fusion with Inverse Covariance Intersection Automatica, vol. 79, pp. 35–41, May, 2017.
In distributed and decentralized state estimation systems, fusion methods are employed to systematically combine multiple estimates of the state into a single, more accurate estimate. An often encountered
problem in the fusion process relates to unknown common information that is shared by the estimates to be fused and is responsible for correlations. If the correlation structure is unknown to the fusion method,
conservative strategies are typically pursued. As such, the parameterization introduced by the ellipsoidal intersection method has been a novel approach to describe unknown correlations, though suitable
values for these parameters with proven consistency have not been identified yet. In this article, an extension of ellipsoidal intersection is proposed that guarantees consistent fusion results in the presence
of unknown common information. The bound used by the novel approach corresponds to computing an outer ellipsoidal bound on the intersection of inverse covariance ellipsoids. As a major advantage of this
inverse covariance intersection method, fusion results prove to be more accurate than those provided by the well-known covariance intersection method.
@article{Automatica17_Noack,
title = {{Decentralized Data Fusion with Inverse Covariance Intersection}},
author = {Benjamin Noack and Joris Sijs and Marc Reinhardt and Uwe D. Hanebeck},
doi = {10.1016/j.automatica.2017.01.019},
journal = {Automatica},
month = may,
pages = {35--41},
volume = {79},
year = {2017}
}
Conferences
Katharina Dormann, Benjamin Noack, Uwe D. Hanebeck
Distributed Kalman Filtering With Reduced Transmission Rate Proceedings of the 2017 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI 2017), Daegu, Korea, November, 2017.
The centralized Kalman filter can be implemented
in such a way that the required calculations can be distributed
over multiple nodes in a network, each of which processes
only the locally acquired sensor data. The main downside of
this implementation is that it requires each distributed sensor
node to communicate with the fusion center in every time step
so as to compute the optimal state estimate. In this paper,
two distributed Kalman filtering algorithms are proposed to
overcome these limitations. The first algorithm merely requires
communication of each local sensor node with the fusion center
in every other time step. The second algorithm even allows
for a lower communicate rate. Both algorithms apply event-based
communication to compute consistent estimates and to
reduce the estimation error for a fixed communication rate.
Simulations demonstrate that both algorithms perform better in
terms of the mean squared estimation error than the centralized
Kalman filter.
@inproceedings{MFI17_Dormann,
title = {{Distributed Kalman Filtering With Reduced Transmission Rate}},
author = {Katharina Dormann and Benjamin Noack and Uwe D. Hanebeck},
booktitle = {Proceedings of the 2017 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI 2017)},
address = {Daegu, Korea},
doi = {10.1109/MFI.2017.8170437},
month = nov,
year = {2017}
}
Florian Pfaff, Gerhard Kurz, Christoph Pieper, Georg Maier, Benjamin Noack, Harald Kruggel-Emden, Robin Gruna, Uwe D. Hanebeck, Siegmar Wirtz, Viktor Scherer, Thomas Längle, Jürgen Beyerer
Improving Multitarget Tracking Using Orientation Estimates for Sorting Bulk Materials Proceedings of the 2017 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI 2017), Daegu, Korea, November, 2017.
Optical belt sorters can be used to sort a large
variety of bulk materials. By the use of sophisticated algo-
rithms, the performance of the complex machinery can be
further improved. Recently, we have proposed an extension
to industrial optical belt sorters that involves tracking the
individual particles on the belt using an area scan camera. If the
estimated behavior of the particles matches the true behavior,
the reliability of the separation process can be improved. The
approach relies on multitarget tracking using hard association
decisions between the tracks and the measurements. In this
paper, we propose to include the orientation in the assessment
of the compatibility of a track and a measurement. This allows
us to achieve more reliable associations, facilitating a higher
accuracy of the tracking results.
@inproceedings{MFI17_Pfaff,
title = {{Improving Multitarget Tracking Using Orientation Estimates for Sorting Bulk Materials}},
author = {Florian Pfaff and Gerhard Kurz and Christoph Pieper and Georg Maier and Benjamin Noack and Harald Kruggel-Emden and Robin Gruna and Uwe D. Hanebeck and Siegmar Wirtz and Viktor Scherer and Thomas L{\"a}ngle and J{\"u}rgen Beyerer},
booktitle = {Proceedings of the 2017 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI 2017)},
address = {Daegu, Korea},
doi = {10.1109/MFI.2017.8170379},
month = nov,
year = {2017}
}
Florian Rosenthal, Benjamin Noack, Uwe D. Hanebeck
State Estimation in Networked Control Systems With Delayed And Lossy Acknowledgments Proceedings of the 2017 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI 2017), Daegu, Korea, November, 2017.
In this paper, we consider state estimation in
Networked Control Systems where both control inputs and
measurements are transmitted via networks which are lossy
and introduce random transmission delays. In contrast to the
common notion of TCP-like communication, where successful
transmissions are acknowledged instantaneously and without
losses, we focus on the case where the acknowledgment packets
provided by the actuator upon reception of applicable control
inputs are also subject to delays and losses. Consequently,
the estimator has only partial and belated knowledge on the
actually applied control inputs, which results in additional
uncertainty. We derive an estimator for the considered setup by
generalizing an existing approach for UDP-like communication
which integrates estimates of the applied control inputs into the
overall state estimation. The presented estimator is assessed in
terms of Monte Carlo simulations.
@inproceedings{MFI17_Rosenthal,
title = {{State Estimation in Networked Control Systems With Delayed And Lossy Acknowledgments}},
author = {Florian Rosenthal and Benjamin Noack and Uwe D. Hanebeck},
booktitle = {Proceedings of the 2017 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI 2017)},
address = {Daegu, Korea},
doi = {10.1109/MFI.2017.8170359},
month = nov,
year = {2017}
}
Christoph Pieper, Georg Maier, Florian Pfaff, Harald Kruggel-Emden, Robin Gruna, Benjamin Noack, Siegmar Wirtz, Viktor Scherer, Thomas Längle, Uwe D. Hanebeck, Jürgen Beyerer
Numerical Modelling of the Separation of Complex Shaped Particles in an Optical Belt Sorter Using a DEM–CFD Approach and Comparison with Experiments V International Conference on Particle-based Methods. Fundamentals and Applications (PARTICLES 2017), Hannover, Germany, September, 2017.
In the growing field of bulk solids handling, automated optical sorting systems are
of increasing importance. However, the initial sorter calibration is still very time consuming
and the precise optical sorting of many materials still remains challenging. In order to
investigate the impact of different operating parameters on the sorting quality, a numerical
model of an existing modular optical belt sorter is presented in this study. The sorter and particle
interaction is described with the Discrete Element Method (DEM) while the air nozzles required
for deflecting undesired material fractions are modelled with Computation Fluid Dynamics
(CFD). The correct representation of the resulting particle–fluid interaction is realized through
a one–way coupling of the DEM with CFD. Complex shaped particle clusters are employed to
model peppercorns also used in experimental investigations. To test the correct implementation
of the utilized models, the particle mass flow within the sorter is compared between experiment
and simulation. The particle separation results of the developed numerical model of the optical
sorting system are compared with matching experimental investigations. The findings show
that the numerical model is able to predict the sorting quality of the optical sorting system with
reasonable accuracy.
@inproceedings{PARTICLES17_Pieper,
title = {{Numerical Modelling of the Separation of Complex Shaped Particles in an Optical Belt Sorter Using a DEM--CFD Approach and Comparison with Experiments}},
author = {Christoph Pieper and Georg Maier and Florian Pfaff and Harald Kruggel-Emden and Robin Gruna and Benjamin Noack and Siegmar Wirtz and Viktor Scherer and Thomas L{\"a}ngle and Uwe D. Hanebeck and J{\"u}rgen Beyerer},
booktitle = {V International Conference on Particle-based Methods. Fundamentals and Applications (PARTICLES 2017)},
address = {Hannover, Germany},
doi = {10.1016/j.powtec.2018.09.003},
month = sep,
year = {2017}
}
Joris Sijs, Benjamin Noack
Event-Based Estimation in a Feedback Loop Anticipating on Imperfect Communication Proceedings of the 20th IFAC World Congress (IFAC 2017), Toulouse, France, July, 2017.
Event-based sampling of sensor signals has become a mature alternative to time-periodic sampling completed with solutions for event-based estimation and control. Among those solutions there is a class of estimators exploiting the fact that an event was not triggered. Not receiving a new measurement is then interpreted as a sensor signal that has not violated the event criteria, which means that the signal is still within the triggering set defining the event. Such implied measurement information is exploited by the estimator, though it is only valid when no event occurred. The approach is thus sensitive to package loss and latency, as the estimator might be incorrect in assuming that no event took place. A solution to anticipate for package loss on the estimation error is studied in this article, and it is further turned into a first solution when the estimator is part of a feedback-control loop.
@inproceedings{IFAC17_Sijs,
title = {{Event-Based Estimation in a Feedback Loop Anticipating on Imperfect Communication}},
author = {Joris Sijs and Benjamin Noack},
booktitle = {Proceedings of the 20th IFAC World Congress (IFAC 2017)},
address = {Toulouse, France},
doi = {10.1016/j.ifacol.2017.08.104},
month = jul,
year = {2017}
}
Florian Pfaff, Benjamin Noack, Uwe D. Hanebeck
Optimal Distributed Combined Stochastic and Set-Membership State Estimation Proceedings of the 20th International Conference on Information Fusion (Fusion 2017), Xi'an, China, July, 2017.
For distributed estimation, algorithms have to be
specifically crafted to minimize communication between the
sensor nodes. As an adjusted version of the regular Kalman filter,
the distributed Kalman filter (DKF) allows for deriving optimal
results while not requiring regular communication. To achieve
this, the DKF requires that each node has full knowledge about
the system model and measurement models of all nodes. However,
the DKF is not sufficient if the characteristics of the errors in the
system and measurement models are not purely stochastic. In this
paper, we present a distributed version of a combined stochastic
and set-membership Kalman filter. The proposed filter optimizes
the approximations of the set-membership uncertainties and can
even yield better results than the regular centralized filter.
@inproceedings{Fusion17_Pfaff-Set,
title = {{Optimal Distributed Combined Stochastic and Set-Membership State Estimation}},
author = {Florian Pfaff and Benjamin Noack and Uwe D. Hanebeck},
booktitle = {Proceedings of the 20th International Conference on Information Fusion (Fusion 2017)},
address = {Xi\textquotesingle an, China},
doi = {10.23919/ICIF.2017.8009723},
month = jul,
year = {2017}
}
Florian Pfaff, Benjamin Noack, Uwe D. Hanebeck, Felix Govaers, Wolfgang Koch
Information Form Distributed Kalman Filtering (IDKF) with Explicit Inputs Proceedings of the 20th International Conference on Information Fusion (Fusion 2017), Xi'an, China, July, 2017.
With the ubiquity of information distributed in
networks, performing recursive Bayesian estimation using
distributed calculations is becoming more and more important.
There are a wide variety of algorithms catering to different
applications and requiring different degrees of knowledge about
the other nodes involved. One recently developed algorithm is
the distributed Kalman filter (DKF), which assumes that all
knowledge about the measurements, except the measurements
themselves, are known to all nodes. If this condition is met,
the DKF allows deriving the optimal estimate if all information
is combined in one node at an arbitrary time step. In this
paper, we present an information form of the distributed Kalman
filter (IDKF) that allows the use of explicit system inputs at
the individual nodes while still yielding the same results as a
centralized Kalman filter.
@inproceedings{Fusion17_Pfaff-IDKF,
title = {{Information Form Distributed Kalman Filtering (IDKF) with Explicit Inputs}},
author = {Florian Pfaff and Benjamin Noack and Uwe D. Hanebeck and Felix Govaers and Wolfgang Koch},
booktitle = {Proceedings of the 20th International Conference on Information Fusion (Fusion 2017)},
address = {Xi\textquotesingle an, China},
doi = {10.23919/ICIF.2017.8009724},
month = jul,
year = {2017}
}
Benjamin Noack, Joris Sijs, Uwe D. Hanebeck
Inverse Covariance Intersection: New Insights and Properties Proceedings of the 20th International Conference on Information Fusion (Fusion 2017), Xi'an, China, July, 2017.
Decentralized data fusion is a challenging task.
Either it is too difficult to maintain and track the information
required to perform fusion optimally, or too much information
is discarded to obtain informative fusion results. A well-known
solution is Covariance Intersection, which may provide too
conservative fusion results. A less conservative alternative is
discussed in this paper, and generalizations are proposed in
order to apply it to a wide class of fusion problems. The Inverse
Covariance Intersection algorithm is about finding the maximum
possible common information shared by the estimates to be
fused. A bound on the possibly shared common information
is derived and removed from the fusion result in order to
guarantee consistency. It is shown that the conditions required
for consistency can be significantly relaxed, and also other causes
of correlations, such as common process noise, can be treated.
@inproceedings{Fusion17_Noack,
title = {{Inverse Covariance Intersection: New Insights and Properties}},
author = {Benjamin Noack and Joris Sijs and Uwe D. Hanebeck},
booktitle = {Proceedings of the 20th International Conference on Information Fusion (Fusion 2017)},
address = {Xi\textquotesingle an, China},
doi = {10.23919/ICIF.2017.8009694},
month = jul,
year = {2017}
}
Georg Maier, Florian Pfaff, Florian Becker, Christoph Pieper, Robin Gruna, Benjamin Noack, Harald Kruggel-Emden, Thomas Längle, Uwe D. Hanebeck, Siegmar Wirtz, Viktor Scherer, Jürgen Beyerer
Improving Material Characterization in Sensor-Based Sorting by Utilizing Motion Information Proceedings of the 3rd Conference on Optical Characterization of Materials (OCM 2017), Karlsruhe, Germany, March, 2017.
Sensor-based sorting provides state-of-the-art solutions for sorting of cohesive, granular materials. Systems tailored to a task at hand, for instance by means of sensors and implementations of data analysis. Conventional systems utilize scanning sensors which do not allow for extraction of motion-related information of objects contained in a material feed. Recently, usage of area-scan cameras to overcome this disadvantage has been proposed. Multitarget tracking can then be used in order to accurately estimate the point in time and position at which any object will reach the separation stage. In this paper, utilizing motion information of objects which can be retrieved from multitarget tracking for the purpose of classification is proposed. Results show that corresponding features can significantly increase classification performance and eventually decrease the detection error of a sorting system.
@inproceedings{OCM17_Maier,
title = {{Improving Material Characterization in Sensor-Based Sorting by Utilizing Motion Information}},
author = {Georg Maier and Florian Pfaff and Florian Becker and Christoph Pieper and Robin Gruna and Benjamin Noack and Harald Kruggel-Emden and Thomas L{\"a}ngle and Uwe D. Hanebeck and Siegmar Wirtz and Viktor Scherer and J{\"u}rgen Beyerer},
booktitle = {Proceedings of the 3rd Conference on Optical Characterization of Materials (OCM 2017)},
address = {Karlsruhe, Germany},
annote = {Winner Best Paper Award},
doi = {10.5445/KSP/1000063696},
month = mar,
url = {https://www.ksp.kit.edu/9783731506126},
year = {2017}
}
2016
Journal Articles
Christoph Pieper, Georg Maier, Florian Pfaff, Harald Kruggel-Emden, Siegmar Wirtz, Robin Gruna, Benjamin Noack, Viktor Scherer, Thomas Längle, Jürgen Beyerer, Uwe D. Hanebeck
Numerical Modeling of an Automated Optical Belt Sorter using the Discrete Element Method Powder Technology, July, 2016.
Optical sorters are important devices in the processing and handling of the globally growing material streams. The precise optical sorting of many bulk solids is still difficult due to the great technical effort necessary for transport and flow control. In this study, particle separation with an automated optical belt sorter is modeled numerically. The Discrete Element Method (DEM) is used to model the sorter and calculate the particle movement as well as particle – particle and particle – wall interactions. The particle ejection stage with air valves is described with the help of a MATLAB script utilizing particle movement information obtained with the DEM. Two models for predicting the particle movement between the detection and separation phase are implemented and compared. In the first model, it is assumed that the particles are moving with belt velocity and without any cross movements and a conventional line scan camera is used for particle detection. In the second model, a more sophisticated approach is employed where the particle motion is predicted with an area scan camera combined with a tracking algorithm. In addition, the influence of different operating parameters like particle shape or conveyor belt length on the separation quality of the system is investigated. Results show that numerical simulations can offer detailed insight into the operation performance of optical sorters and help to optimize operating parameters. The area scan camera approach was found to be superior to the standard line scan camera model in almost all investigated categories.
@article{PowTec16_Pieper,
title = {{Numerical Modeling of an Automated Optical Belt Sorter using the Discrete Element Method}},
author = {Christoph Pieper and Georg Maier and Florian Pfaff and Harald Kruggel-Emden and Siegmar Wirtz and Robin Gruna and Benjamin Noack and Viktor Scherer and Thomas L{\"a}ngle and J{\"u}rgen Beyerer and Uwe D. Hanebeck},
doi = {10.1016/j.powtec.2016.07.018},
journal = {Powder Technology},
month = jul,
year = {2016}
}
Florian Pfaff, Christoph Pieper, Georg Maier, Benjamin Noack, Harald Kruggel-Emden, Robin Gruna, Uwe D. Hanebeck, Siegmar Wirtz, Viktor Scherer, Thomas Längle, Jürgen Beyerer
Improving Optical Sorting of Bulk Materials Using Sophisticated Motion Models tm - Technisches Messen, De Gruyter, vol. 83, no. 2, pp. 77–84, February, 2016.
Visual properties are powerful features to
reliably classify bulk materials, thereby allowing to detect
defect or low quality particles. Optical belt sorters are
an established technology to sort based on these properties,
but they suffer from delays between the simultaneous
classification and localization step and the subsequent
separation step. Therefore, accurate models to predict the
particles’ motions are a necessity to bridge this gap. In
this paper, we explicate our concept to use sophisticated
simulations to derive accurate models and optimize the
flow of bulk solids via adjustments of the sorter design.
This allows us to improve overall sorting accuracy and
cost efficiency. Lastly, initial results are presented.
@article{TM16_Pfaff,
title = {{Improving Optical Sorting of Bulk Materials Using Sophisticated Motion Models}},
author = {Florian Pfaff and Christoph Pieper and Georg Maier and Benjamin Noack and Harald Kruggel-Emden and Robin Gruna and Uwe D. Hanebeck and Siegmar Wirtz and Viktor Scherer and Thomas L{\"a}ngle and J{\"u}rgen Beyerer},
doi = {10.1515/teme-2015-0108},
journal = {tm - Technisches Messen, De Gruyter},
month = feb,
number = {2},
pages = {77--84},
url = {http://www.degruyter.com/view/j/teme.2016.83.issue-2/teme-2015-0108/teme-2015-0108.xml},
volume = {83},
year = {2016}
}
Conferences
Florian Faion, Antonio Zea, Benjamin Noack, Jannik Steinbring, Uwe D. Hanebeck
Camera- and IMU-based Pose Tracking for Augmented Reality Proceedings of the 2016 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI 2016), Baden-Baden, Germany, September, 2016.
In this paper, we propose an algorithm for
tracking mobile devices (such as smartphones, tablets, or
smartglasses) in a known environment for augmented reality
applications. For this purpose, we interpret the environment as
an extended object with a known shape, and design likelihoods
for different types of image features, using association models
from extended object tracking. Based on these likelihoods, and
together with sensor information of the inertial measurement
unit of the mobile device, we design a recursive Bayesian
tracking algorithm. We present results of our first prototype
and discuss the lessons we learned from its implementation.
In particular, we set up a “pick-by-vision” scenario, where the
location of objects in a shelf is to be highlighted in a camera
image. Our experiments confirm that the proposed tracking
approach achieves accurate and robust tracking results even in
scenarios with fast motion.
@inproceedings{MFI16_Faion,
title = {{Camera- and IMU-based Pose Tracking for Augmented Reality}},
author = {Florian Faion and Antonio Zea and Benjamin Noack and Jannik Steinbring and Uwe D. Hanebeck},
booktitle = {Proceedings of the 2016 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI 2016)},
address = {Baden-Baden, Germany},
doi = {10.1109/MFI.2016.7849560},
month = sep,
year = {2016}
}
Georg Maier, Florian Pfaff, Christoph Pieper, Robin Gruna, Benjamin Noack, Harald Kruggel-Emden, Thomas Längle, Uwe D. Hanebeck, Siegmar Wirtz, Viktor Scherer, Jürgen Beyerer
Fast Multitarget Tracking via Strategy Switching for Sensor-Based Sorting Proceedings of the 2016 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI 2016), Baden-Baden, Germany, September, 2016.
State-of-the-art sensor-based sorting systems provide solutions to sort various products according to quality
aspects. Such systems face the challenge of an existing delay
between perception and separation of the material. To reliably
predict an object's position when reaching the separation
stage, information regarding its movement needs to be derived.
Multitarget tracking offers approaches through which this
can be achieved. However, processing time is typically limited
since the sorting decision for each object needs to be derived
sufficiently early before it reaches the separation stage. In this
paper, an approach for multitarget tracking in sensor-based
sorting is proposed which supports establishing an upper bound
regarding processing time required for solving the measurement
to track association problem. To demonstrate the success of
the proposed method, experiments are conducted for data-sets
obtained via simulation of a sorting system. This way, it
is possible to not only demonstrate the impact on required
runtime but also on the quality of the association.
@inproceedings{MFI16_Maier,
title = {{Fast Multitarget Tracking via Strategy Switching for Sensor-Based Sorting}},
author = {Georg Maier and Florian Pfaff and Christoph Pieper and Robin Gruna and Benjamin Noack and Harald Kruggel-Emden and Thomas L{\"a}ngle and Uwe D. Hanebeck and Siegmar Wirtz and Viktor Scherer and J{\"u}rgen Beyerer},
booktitle = {Proceedings of the 2016 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI 2016)},
address = {Baden-Baden, Germany},
doi = {10.1109/MFI.2016.7849538},
month = sep,
year = {2016}
}
Benjamin Noack, Joris Sijs, Uwe D. Hanebeck
Algebraic Analysis of Data Fusion with Ellipsoidal Intersection Proceedings of the 2016 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI 2016), Baden-Baden, Germany, September, 2016.
For decentralized fusion problems, ellipsoidal intersection has been proposed as an efficient fusion rule that provides less conservative results as compared to the well-know covariance intersection method. Ellipsoidal intersection relies on the computation of a common estimate that is shared by the estimates to be fused. In this paper, an algebraic reformulation of ellipsoidal intersection is discussed that circumvents the computation of the common estimate. It is shown that ellipsoidal intersection corresponds to an internal ellipsoidal approximation of the intersection of covariance ellipsoids. An interesting result is that ellipsoidal intersection can be computed with the aid of the Bar-Shalom/Campo fusion formulae. This is achieved by assuming a specific correlation structure between the estimates to be fused.
@inproceedings{MFI16_Noack,
title = {{Algebraic Analysis of Data Fusion with Ellipsoidal Intersection}},
author = {Benjamin Noack and Joris Sijs and Uwe D. Hanebeck},
booktitle = {Proceedings of the 2016 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI 2016)},
address = {Baden-Baden, Germany},
doi = {10.1109/MFI.2016.7849515},
month = sep,
year = {2016}
}
Florian Pfaff, Christoph Pieper, Georg Maier, Benjamin Noack, Harald Kruggel-Emden, Robin Gruna, Uwe D. Hanebeck, Siegmar Wirtz, Viktor Scherer, Thomas Längle, Jürgen Beyerer
Simulation-based Evaluation of Predictive Tracking for Sorting Bulk Materials Proceedings of the 2016 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI 2016), Baden-Baden, Germany, September, 2016.
Multitarget tracking problems arise in many real-world
applications. The performance of the utilized algorithm
strongly depends both on how the data association problem is
handled and on the suitability of the motion models employed.
Especially the motion models can be hard to validate. Previously,
we have proposed to use multitarget tracking to improve optical
belt sorters. In this paper, we evaluate both the suitability of
our model and the tracking and then of our entire system
incorporating the image processing component via the use of
highly realistic numerical simulations. We first assess the model
using noise-free measurements generated by the simulation and
then evaluate the entire system by using synthetically generated
image data.
@inproceedings{MFI16_Pfaff,
title = {{Simulation-based Evaluation of Predictive Tracking for Sorting Bulk Materials}},
author = {Florian Pfaff and Christoph Pieper and Georg Maier and Benjamin Noack and Harald Kruggel-Emden and Robin Gruna and Uwe D. Hanebeck and Siegmar Wirtz and Viktor Scherer and Thomas L{\"a}ngle and J{\"u}rgen Beyerer},
booktitle = {Proceedings of the 2016 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI 2016)},
address = {Baden-Baden, Germany},
doi = {10.1109/MFI.2016.7849539},
month = sep,
year = {2016}
}
Christoph Pieper, Harald Kruggel-Emden, Siegmar Wirtz, Viktor Scherer, Florian Pfaff, Benjamin Noack, Uwe D. Hanebeck, Georg Maier, Robin Gruna, Thomas Längle, Jürgen Beyerer
Numerical Investigation of Optical Sorting using the Discrete Element Method Proceedings of the 7th International Conference on Discrete Element Methods (DEM7), Dalian, China, August, 2016.
Automated optical sorting systems are important devices in the growing field of bulk solids handling. The initial sorter calibration and the precise optical sorting of many materials is still very time consuming and difficult. A numerical model of an automated optical belt sorter is presented in this study. The sorter and particle interaction is described with the Discrete Element Method (DEM) while
the separation phase is considered in a post processing step. Different operating parameters and their influence on sorting quality are investigated. In addition, two models for detecting and predicting the particle movement between the detection point and the separation step are presented and compared, namely a conventional line scan camera model and a new approach combining an area scan camera model with particle tracking.
@inproceedings{DEM16_Pieper,
title = {{Numerical Investigation of Optical Sorting using the Discrete Element Method}},
author = {Christoph Pieper and Harald Kruggel-Emden and Siegmar Wirtz and Viktor Scherer and Florian Pfaff and Benjamin Noack and Uwe D. Hanebeck and Georg Maier and Robin Gruna and Thomas L{\"a}ngle and J{\"u}rgen Beyerer},
booktitle = {Proceedings of the 7th International Conference on Discrete Element Methods (DEM7)},
address = {Dalian, China},
doi = {10.1007/978-981-10-1926-5_115},
month = aug,
year = {2016}
}
Benjamin Noack, Florian Pfaff, Marcus Baum, Uwe D. Hanebeck
State Estimation Considering Negative Information with Switching Kalman and Ellipsoidal Filtering Proceedings of the 19th International Conference on Information Fusion (Fusion 2016), Heidelberg, Germany, July, 2016.
State estimation concepts like the Kalman filter heavily rely on potentially noisy sensor data. In general, the estimation quality depends on the amount of sensor data that can be exploited. However, missing observations do not necessarily impair the estimation quality but may also convey exploitable information on the system state. This type of information - noted as negative information - often requires specific measurement and noise models in order to take advantage of it. In this paper, a hybrid Kalman filter concept is employed that allows using both stochastic and set-membership representations of information. In particular, the latter representation is intended to account for negative information, which can often be easily described as a bounded set in the measurement space. Depending on the type of information, the filtering step of the proposed estimator adaptively switches between Gaussian and ellipsoidal noise representations. A target tracking scenario is studied to evaluate and discuss the proposed concept.
@inproceedings{Fusion16_Noack,
title = {{State Estimation Considering Negative Information with Switching Kalman and Ellipsoidal Filtering}},
author = {Benjamin Noack and Florian Pfaff and Marcus Baum and Uwe D. Hanebeck},
booktitle = {Proceedings of the 19th International Conference on Information Fusion (Fusion 2016)},
address = {Heidelberg, Germany},
month = jul,
url = {https://ieeexplore.ieee.org/document/7528121},
year = {2016}
}
Jannik Steinbring, Benjamin Noack, Marc Reinhardt, Uwe D. Hanebeck
Optimal Sample-Based Fusion for Distributed State Estimation Proceedings of the 19th International Conference on Information Fusion (Fusion 2016), Heidelberg, Germany, July, 2016.
In this paper, we present a novel approach to
optimally fuse estimates in distributed state estimation for linear
and nonlinear systems. An optimal fusion requires the knowledge
of the correct correlations between locally obtained estimates.
The naive and intractable way of calculating the correct
correlations would be to exchange information about every processed
measurement between all nodes. Instead, we propose to obtain
the correct correlations by keeping and processing a small set
of deterministic samples on each node in parallel to the actual
local state estimation. Sending these samples in addition to the
local state estimate to the fusion center allows for correctly
reconstructing the desired correlations between all estimates.
In doing so, each node does not need any information about
measurements processed on other nodes. We show the optimality
of the proposed method by means of tracking an extended object
in a multi-camera network.
@inproceedings{Fusion16_Steinbring,
title = {{Optimal Sample-Based Fusion for Distributed State Estimation}},
author = {Jannik Steinbring and Benjamin Noack and Marc Reinhardt and Uwe D. Hanebeck},
booktitle = {Proceedings of the 19th International Conference on Information Fusion (Fusion 2016)},
address = {Heidelberg, Germany},
month = jul,
url = {https://ieeexplore.ieee.org/document/7528074},
year = {2016}
}
Benjamin Noack, Uwe D. Hanebeck
State Estimation Using Virtual Measurement Information Proceedings of the 18. GMA/ITG Fachtagung Sensoren und Messsysteme 2016, May, 2016.
The computation of an estimate for the unknown state of a dynamical system is a central challenge in many disciplines and applications. In general, the estimation quality is directly tied to the amount of sensor data available to the state estimation system. However, insights from virtual or missing observations may also convey exploitable information on the system’s state. Such virtual measurement information may relate to constraints to which the state is subject. For instance, constraints to acceleration and turn rate of a mobile robot may apply and can be exploited. Analogously, missing observations that are attributable to obstacles can be translated into usable information, which is often referred to as negative sensor evidence. Such implicit information has to be reformulated into virtual measurement data in order to take advantage of it. As the Kalman filter and its derivatives are most widely used in state estimation applications, specific measurement and noise models for virtual observations are to be derived that can easily be integrated into the prediction-correction cycle of the Kalman filter. In this work, a set-membership representation of virtual measurement information is discussed.
@inproceedings{Sensoren2016_Noack,
title = {{State Estimation Using Virtual Measurement Information}},
author = {Benjamin Noack and Uwe D. Hanebeck},
booktitle = {Proceedings of the 18. GMA/ITG Fachtagung Sensoren und Messsysteme 2016},
doi = {10.5162/sensoren2016/1.3.3},
month = may,
year = {2016}
}
2015
Book Chapters
Joris Sijs, Benjamin Noack, Mircea Lazar, Uwe D. Hanebeck
Time-Periodic State Estimation with Event-Based Measurement Updates Event-Based Control and Signal Processing, pp. 261–279, CRC Press, November, 2015.
To reduce the amount of data transfers
in networked systems, measurements can be taken at
an event on the sensor value rather than periodically
in time. Yet, this could lead to a divergence of estimation results when only the received measurement
values are exploited in a state estimation procedure.
A solution to this issue has been found by developing
estimators that perform a state update at both the event
instants as well as periodically in time: when an event
occurs the estimated state is updated using the measurement received, while at periodic instants the update is
based on knowledge that the sensor value lies within a
bounded subset of the measurement space. Several solutions for event-based state estimation will be presented
in this chapter, either based on stochastic representations
of random vectors, on deterministic representations of
random vectors or on a mixture of the two. All solutions aim to limit the required computational resources
by deriving explicit solutions for computing estimation
results. Yet, the main achievement for each estimation
solution is that stability of the estimation results are (not directly) dependent on the employed event sampling
strategy. As such, changing the event sampling strategy does not imply to change the event-based estimator
as well. This aspect is also illustrated in a case study
of tracking the distribution of a chemical compound
effected by wind via a wireless sensor network.
@incollection{CRC15_Sijs,
title = {{Time-Periodic State Estimation with Event-Based Measurement Updates}},
author = {Joris Sijs and Benjamin Noack and Mircea Lazar and Uwe D. Hanebeck},
booktitle = {Event-Based Control and Signal Processing},
doi = {10.1201/b19013},
editor = {Marek Miskowicz},
month = nov,
pages = {261--279},
publisher = {CRC Press},
url = {http://www.crcnetbase.com/isbn/9781482256567},
year = {2015}
}
Benjamin Noack, Joris Sijs, Marc Reinhardt, Uwe D. Hanebeck
Treatment of Dependent Information in Multisensor Kalman Filtering and Data Fusion Multisensor Data Fusion: From Algorithms and Architectural Design to Applications, pp. 169–192, CRC Press, August, 2015.
Distributed and decentralized processing and fusion of sensor data are becoming increasingly important. In view of the Internet of Things and the vision of ubiquitous sensing, designing and implementing multisensor state estimation algorithm have already become a key issue. A network of interconnected sensor devices is usually characterized by the idea to process and collect data locally and independently on the sensor nodes. However, this does not imply that the data are independent of each other, and the state estimation algorithms have to address possible interdependencies so as to avoid erroneous data fusion results.
Dependencies among local estimates generally can be traced back to common sensor information and common process noise. A wide variety of Kalman filtering schemes allow for the treatment of dependent data in centralized, distributed, and decentralized networks of sensor nodes, but making the right choice is itself dependent upon analyzing and weighing up the different advantages and disadvantages. This chapter discusses different strategies to identify and treat dependencies among Kalman filter estimates while pointing out advantages and challenges.
@incollection{CRC15_Noack,
title = {{Treatment of Dependent Information in Multisensor Kalman Filtering and Data Fusion}},
author = {Benjamin Noack and Joris Sijs and Marc Reinhardt and Uwe D. Hanebeck},
booktitle = {Multisensor Data Fusion: From Algorithms and Architectural Design to Applications},
doi = {10.1201/b18851},
editor = {Hassen Fourati},
month = aug,
pages = {169--192},
publisher = {CRC Press},
url = {http://www.crcnetbase.com/doi/book/10.1201/b18851},
year = {2015}
}
Journal Articles
Marc Reinhardt, Benjamin Noack, Pablo O. Arambel, Uwe D. Hanebeck
Minimum Covariance Bounds for the Fusion under Unknown Correlations IEEE Signal Processing Letters, vol. 22, no. 9, pp. 1210–1214, September, 2015.
One of the key challenges in distributed linear estimation is the systematic fusion of estimates. While the fusion gains that minimize the mean squared error of the fused estimate for known correlations have been established, no analogous statement could be obtained so far for unknown correlations. In this contribution, we derive the gains that minimize the bound on the true covariance of the fused estimate and prove that Covariance Intersection (CI) is the optimal bounding algorithm for two estimates under completely unknown correlations. When combining three or more variables, the CI equations are not necessarily optimal, as shown by a counterexample.
@article{SPL15_Reinhardt,
title = {{Minimum Covariance Bounds for the Fusion under Unknown Correlations}},
author = {Marc Reinhardt and Benjamin Noack and Pablo O. Arambel and Uwe D. Hanebeck},
doi = {10.1109/LSP.2015.2390417},
journal = {IEEE Signal Processing Letters},
month = sep,
number = {9},
pages = {1210--1214},
volume = {22},
year = {2015}
}
Conferences
Marcus Baum, Benjamin Noack, Uwe D. Hanebeck
Kalman Filter-based SLAM with Unknown Data Association using Symmetric Measurement Equations Proceedings of the 2015 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI 2015), San Diego, California, USA, September, 2015.
This work investigates a novel method for dealing with unknown data associations in Kalman filter-based Simultaneous Localization and Mapping (SLAM) problems. The key idea is to employ the concept of Symmetric Measurement Equations (SMEs) in order to remove the data association uncertainty from the original measurement equation. Based on the resulting modified measurement equation, standard nonlinear Kalman filters can estimate the full joint state vector of the robot and landmarks without explicitly calculating data association hypotheses.
@inproceedings{MFI15_Baum,
title = {{Kalman Filter-based SLAM with Unknown Data Association using Symmetric Measurement Equations}},
author = {Marcus Baum and Benjamin Noack and Uwe D. Hanebeck},
booktitle = {Proceedings of the 2015 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI 2015)},
address = {San Diego, California, USA},
doi = {10.1109/MFI.2015.7295744},
month = sep,
year = {2015}
}
Benjamin Noack, Marcus Baum, Uwe D. Hanebeck
State Estimation for Ellipsoidally Constrained Dynamic Systems with Set-membership Pseudo Measurements Proceedings of the 2015 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI 2015), San Diego, California, USA, September, 2015.
In many dynamic systems, the evolution of the state is subject to specific constraints. In general, constraints cannot easily be integrated into the prediction-correction structure of the Kalman filter algorithm. Linear equality constraints are an exception to this rule and have been widely used and studied as they allow for simple closed-form expressions. A common approach is to reformulate equality constraints into pseudo measurements of the state to be estimated. However, equality constraints define deterministic relationships between state components which is an undesirable property in Kalman filtering as this leads to singular covariance matrices. A second problem relates to the knowledge required to identify and define precise constraints, which are met by the system state. In this article, ellipsoidal constraints are introduced that can be employed to model a bounded region, to which the system state is constrained. This concept constitutes an easy-to-use relaxation of equality constraints. In order to integrate ellipsoidal constraints into the Kalman filter structure, a generalized filter framework is utilized that relies on a combined stochastic and set-membership uncertainty representation.
@inproceedings{MFI15_Noack,
title = {{State Estimation for Ellipsoidally Constrained Dynamic Systems with Set-membership Pseudo Measurements}},
author = {Benjamin Noack and Marcus Baum and Uwe D. Hanebeck},
booktitle = {Proceedings of the 2015 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI 2015)},
address = {San Diego, California, USA},
doi = {10.1109/MFI.2015.7295824},
month = sep,
year = {2015}
}
Florian Pfaff, Marcus Baum, Benjamin Noack, Uwe D. Hanebeck, Robin Gruna, Thomas Längle, Jürgen Beyerer
TrackSort: Predictive Tracking for Sorting Uncooperative Bulk Materials Proceedings of the 2015 IEEE International Conference on Multisensor Fusion and Information Integration (MFI 2015), San Diego, California, USA, September, 2015.
Optical belt sorters are a versatile, state-of-the-art technology to sort bulk materials that are hard to sort based on only nonvisual properties. In this paper, we propose an extension to current optical belt sorters that involves replacing the line camera with an area camera to observe a wider field of view, allowing us to observe each particle over multiple time steps. By performing multitarget tracking, we are able to improve the prediction of each particle's movement and thus enhance the performance of the utilized separation mechanism. We show that our approach will allow belt sorters to handle new classes of bulk materials while improving cost efficiency. Furthermore, we lay out additional extensions that are made possible by our new paradigm
@inproceedings{MFI15_Pfaff,
title = {{TrackSort: Predictive Tracking for Sorting Uncooperative Bulk Materials}},
author = {Florian Pfaff and Marcus Baum and Benjamin Noack and Uwe D. Hanebeck and Robin Gruna and Thomas L{\"a}ngle and J{\"u}rgen Beyerer},
booktitle = {Proceedings of the 2015 IEEE International Conference on Multisensor Fusion and Information Integration (MFI 2015)},
address = {San Diego, California, USA},
doi = {10.1109/MFI.2015.7295737},
month = sep,
year = {2015}
}
Benjamin Noack, Simon J. Julier, Uwe D. Hanebeck
Treatment of Biased and Dependent Sensor Data in Graph-based SLAM Proceedings of the 18th International Conference on Information Fusion (Fusion 2015), Washington D. C., USA, July, 2015.
A common approach to attack the simultaneous localization and mapping problem (SLAM) is to consider factor-graph formulations of the underlying filtering and estimation setup. While Kalman filter-based methods provide an estimate for the current pose of a robot and all landmark positions, graph-based approaches take not only the current pose into account but also the entire trajectory of the robot and have to solve a nonlinear least-squares optimization problem. Using graph-based representations has proven to be highly scalable and very accurate as compared with traditional filter-based approaches. However, biased measurements as well as unmodeled correlations can lead to a sharp deterioration in the estimation quality and hence require careful consideration. In this paper, a method to incorporate biased or dependent measurement information is proposed that can easily be integrated into existing optimization algorithms for graph-based SLAM. For biased sensor data, techniques from ellipsoidal calculus are employed to compute the corresponding information matrices. Dependencies among noise terms are treated by a generalization of the covariance intersection concept. The treatment of both biased and correlated sensor data rest upon the inflation of the involved error matrices. Simulations are used to discuss and evaluate the proposed method.
@inproceedings{Fusion15_Noack,
title = {{Treatment of Biased and Dependent Sensor Data in Graph-based SLAM}},
author = {Benjamin Noack and Simon J. Julier and Uwe D. Hanebeck},
booktitle = {Proceedings of the 18th International Conference on Information Fusion (Fusion 2015)},
address = {Washington D. C., USA},
month = jul,
url = {https://ieeexplore.ieee.org/document/7266782},
year = {2015}
}
2014
Conferences
Benjamin Noack, Joris Sijs, Uwe D. Hanebeck
Fusion Strategies for Unequal State Vectors in Distributed Kalman Filtering Proceedings of the 19th IFAC World Congress (IFAC 2014), Cape Town, South Africa, August, 2014.
Distributed implementations of state estimation algorithms generally have in common that each node in a networked system computes an estimate on the entire global state. Accordingly, each node has to store and compute an estimate of the same state vector irrespective of whether its sensors can only observe a small part of it. In particular, the task of monitoring large-scale phenomena renders such distributed estimation approaches impractical due to the sheer size of the corresponding state vector. In order to reduce the workload of the nodes, the state vector to be estimated is subdivided into smaller, possibly overlapping parts. In this situation, fusion does not only refer to the computation of an improved estimate but also to the task of reassembling an estimate for the entire state from the locally computed estimates of unequal state vectors. However, existing fusion methods require equal state representations and, hence, cannot be employed. For that reason, a fusion strategy for estimates of unequal and possibly overlapping state vectors is derived that minimizes the mean squared estimation error. For the situation of unknown cross-correlations between local estimation errors, also a conservative fusion strategy is proposed.
@inproceedings{IFAC14_Noack,
title = {{Fusion Strategies for Unequal State Vectors in Distributed Kalman Filtering}},
author = {Benjamin Noack and Joris Sijs and Uwe D. Hanebeck},
booktitle = {Proceedings of the 19th IFAC World Congress (IFAC 2014)},
address = {Cape Town, South Africa},
doi = {10.3182/20140824-6-ZA-1003.02491},
month = aug,
year = {2014}
}
Jiří Ajgl, Miroslav Šimandl, Marc Reinhardt, Benjamin Noack, Uwe D. Hanebeck
Covariance Intersection in State Estimation of Dynamical Systems Proceedings of the 17th International Conference on Information Fusion (Fusion 2014), Salamanca, Spain, July, 2014.
The Covariance Intersection algorithm linearly combines estimates when the cross-correlations between their errors are unknown. It provides a fused estimate and an upper bound of the corresponding mean square error matrix. The weights of the linear combination are designed in order to minimise the upper bound. This paper analyses the optimal weights in relation to state estimation of dynamical systems. It is shown that the use of the optimal upper bound in a standard recursive filtering does not lead to optimal upper bounds in subsequent processing steps. Unlike the fusion under full knowledge, the fusion under unknown cross-correlations can fuse the same information differently, depending on the independent information that will be available in the future.
@inproceedings{Fusion14_Ajgl,
title = {{Covariance Intersection in State Estimation of Dynamical Systems}},
author = {Ji{\v r}{\'\i} Ajgl and Miroslav {\v S}imandl and Marc Reinhardt and Benjamin Noack and Uwe D. Hanebeck},
booktitle = {Proceedings of the 17th International Conference on Information Fusion (Fusion 2014)},
address = {Salamanca, Spain},
month = jul,
url = {https://ieeexplore.ieee.org/document/6916138},
year = {2014}
}
Benjamin Noack, Marc Reinhardt, Uwe D. Hanebeck
On Nonlinear Track-to-track Fusion with Gaussian Mixtures Proceedings of the 17th International Conference on Information Fusion (Fusion 2014), Salamanca, Spain, July, 2014.
The problem of fusing state estimates is encountered in many network-based multi-sensor applications. The majority of distributed state estimation algorithms are designed to provide multiple estimates on the same state, and track-to-track fusion then refers to the task of combining these estimates. While linear fusion only requires the joint cross-covariance matrix to be known, dependencies between estimates in nonlinear estimation problems have to be represented by high-dimensional probability density functions. In general, storing and keeping track of nonlinear dependencies is too cumbersome. However, this paper demonstrates that estimates represented by Gaussian mixtures prove to be an important exception to this rule. The dependency structure can as well be characterized in terms of a higher-dimensional Gaussian mixture. The different processing steps of distributed nonlinear state estimation, i.e., prediction, filtering, and fusion, are studied in light of the joint density representation. The presented concept is complemented with different simpler suboptimal representations of the dependency structure between Gaussian mixture densities.
@inproceedings{Fusion14_Noack,
title = {{On Nonlinear Track-to-track Fusion with Gaussian Mixtures}},
author = {Benjamin Noack and Marc Reinhardt and Uwe D. Hanebeck},
booktitle = {Proceedings of the 17th International Conference on Information Fusion (Fusion 2014)},
address = {Salamanca, Spain},
month = jul,
url = {https://ieeexplore.ieee.org/document/6916008},
year = {2014}
}
Marc Reinhardt, Benjamin Noack, Sanjeev Kulkarni, Uwe D. Hanebeck
Distributed Kalman Filtering in the Presence of Packet Delays and Losses Proceedings of the 17th International Conference on Information Fusion (Fusion 2014), Salamanca, Spain, July, 2014.
Distributed Kalman filtering aims at optimizing an estimate at a fusion center based on information that is gathered in a sensor network. Recently, an exact solution based on local estimation tracks has been proposed and an extension to cope with packet losses has been derived. In this contribution, we generalize both algorithms to packet delays. The key idea is to introduce augmented measurement vectors in the sensors that permit the optimization of local filter gains according to time-dependent measurement capabilities at the fusion center. In the most general form, the algorithm provides optimized estimates in sensor networks with packets delays and losses. The precision depends on the actual arrival patterns, and the results correspond to those of the centralized Kalman filter when specific assumptions about the measurement capability are satisfied.
@inproceedings{Fusion14_Reinhardt,
title = {{Distributed Kalman Filtering in the Presence of Packet Delays and Losses}},
author = {Marc Reinhardt and Benjamin Noack and Sanjeev Kulkarni and Uwe D. Hanebeck},
booktitle = {Proceedings of the 17th International Conference on Information Fusion (Fusion 2014)},
address = {Salamanca, Spain},
month = jul,
url = {https://ieeexplore.ieee.org/document/6915998},
year = {2014}
}
Joris Sijs, Leon Kester, Benjamin Noack
A Study on Event Triggering Criteria for Estimation Proceedings of the 17th International Conference on Information Fusion (Fusion 2014), Salamanca, Spain, July, 2014.
To reduce the amount of data transfer in networked systems measurements are usually taken only when an event occurs rather than periodically in time. However, a fundamental assessment on the response of estimation algorithms receiving event sampled measurements is not available. This research presents such an analysis when new measurements are sampled at well-designed events and sent to a Luenberger observer. Conditions are then derived under which the estimation error is bounded, followed by an assessment of two event sampling strategies when the estimator encounters two different types of disturbances: an impulse and a step disturbance. The sampling strategies are compared via four performance measures, such as estimation-error and communication resources. The result is a clear insight of the estimation response in an event-based setup.
@inproceedings{Fusion14_Sijs,
title = {{A Study on Event Triggering Criteria for Estimation}},
author = {Joris Sijs and Leon Kester and Benjamin Noack},
booktitle = {Proceedings of the 17th International Conference on Information Fusion (Fusion 2014)},
address = {Salamanca, Spain},
month = jul,
url = {https://ieeexplore.ieee.org/document/6916231},
year = {2014}
}
Marc Reinhardt, Benjamin Noack, Uwe D. Hanebeck
Reconstruction of Joint Covariance Matrices in Networked Linear Systems Proceedings of the 48th Annual Conference on Information Sciences and Systems (CISS 2014), Princeton, New Jersey, USA, March, 2014.
In this paper, a sample representation of the estimation error is utilized to reconstruct the joint covariance matrix in a distributed estimation system. The key idea is to sample uncorrelated and fully correlated noise according to different techniques at local estimators without knowledge about the processing of other nodes in the network. This way, the correlation between estimates is inherently linked to the representation of the corresponding sample sets. We discuss the noise processing, derive key attributes, and evaluate the precision of the covariance estimates.
@inproceedings{CISS14_Reinhardt,
title = {{Reconstruction of Joint Covariance Matrices in Networked Linear Systems}},
author = {Marc Reinhardt and Benjamin Noack and Uwe D. Hanebeck},
booktitle = {Proceedings of the 48th Annual Conference on Information Sciences and Systems (CISS 2014)},
address = {Princeton, New Jersey, USA},
doi = {10.1109/CISS.2014.6814071},
month = mar,
year = {2014}
}
2013
Conferences
Benjamin Noack, Simon J. Julier, Marc Reinhardt, Uwe D. Hanebeck
Nonlinear Federated Filtering Proceedings of the 16th International Conference on Information Fusion (Fusion 2013), Istanbul, Turkey, July, 2013.
The federated Kalman filter embodies an efficient and easy-to-implement solution for linear distributed estimation problems. Data from independent sensors can be processed locally and in parallel on different nodes without running the risk of erroneously ignoring possible dependencies. The underlying idea is to counteract the common process noise issue by inflating the joint process noise matrix. In this paper, the same trick is generalized to nonlinear models and non-Gaussian process noise. The probability density of the joint process noise is split into an exponential mixture of transition densities. By this means, the process noise is modeled to independently affect the local system models. The estimation results provided by the sensor devices can then be fused, just as if they were indeed independent.
@inproceedings{Fusion13_Noack,
title = {{Nonlinear Federated Filtering}},
author = {Benjamin Noack and Simon J. Julier and Marc Reinhardt and Uwe D. Hanebeck},
booktitle = {Proceedings of the 16th International Conference on Information Fusion (Fusion 2013)},
address = {Istanbul, Turkey},
month = jul,
url = {https://ieeexplore.ieee.org/document/6641299},
year = {2013}
}
Florian Pfaff, Benjamin Noack, Uwe D. Hanebeck
Data Validation in the Presence of Stochastic and Set-membership Uncertainties Proceedings of the 16th International Conference on Information Fusion (Fusion 2013), Istanbul, Turkey, July, 2013.
For systems suffering from different types of uncertainties, finding criteria for validating measurements can be challenging. In this paper, we regard both stochastic Gaussian noise with full or imprecise knowledge about correlations and unknown but bounded errors. The validation problems arising in the individual and combined cases are illustrated to convey different perspectives on the proposed conditions. Furthermore, hints are provided for the algorithmic implementation of the validation tests. Particular focus is put on ensuring a predefined lower bound for the probability of correctly classifying valid data.
@inproceedings{Fusion13_Pfaff,
title = {{Data Validation in the Presence of Stochastic and Set-membership Uncertainties}},
author = {Florian Pfaff and Benjamin Noack and Uwe D. Hanebeck},
booktitle = {Proceedings of the 16th International Conference on Information Fusion (Fusion 2013)},
address = {Istanbul, Turkey},
month = jul,
url = {https://ieeexplore.ieee.org/document/6641269},
year = {2013}
}
Marc Reinhardt, Benjamin Noack, Uwe D. Hanebeck
Advances in Hypothesizing Distributed Kalman Filtering Proceedings of the 16th International Conference on Information Fusion (Fusion 2013), Istanbul, Turkey, July, 2013.
In this paper, linear distributed estimation is revisited on the basis of the hypothesizing distributed Kalman filter and equations for a flexible application of the algorithm are derived. We propose a new approximation for the mean-squared-error matrix and present techniques for automatically improving the hypothesis about the global measurement model. Utilizing these extensions, the precision of the filter is improved so that it asymptotically yields optimal results for time-invariant models. Pseudo-code for the implementation of the algorithm is provided and the lossless inclusion of out-of-sequence measurements is discussed. An evaluation demonstrates the effect of the new extensions and compares the results to state-of-the-art methods.
@inproceedings{Fusion13_Reinhardt,
title = {{Advances in Hypothesizing Distributed Kalman Filtering}},
author = {Marc Reinhardt and Benjamin Noack and Uwe D. Hanebeck},
booktitle = {Proceedings of the 16th International Conference on Information Fusion (Fusion 2013)},
address = {Istanbul, Turkey},
month = jul,
url = {https://ieeexplore.ieee.org/document/6641078},
year = {2013}
}
Joris Sijs, Uwe D. Hanebeck, Benjamin Noack
An Empirical Method to Fuse Partially Overlapping State Vectors for Distributed State Estimation Proceedings of the 2013 European Control Conference (ECC 2013), Zürich, Switzerland, July, 2013.
State fusion is a method for merging multiple estimates of the same state into a single fused estimate. Dealing with multiple estimates is one of the main concerns in distributed state estimation, where an estimated value of the desired state vector is computed in each node of a networked system. Most solutions for distributed state estimation currently available assume that every node computes an estimate of the (same) global state vector. This assumption is impractical for systems observing large-area processes, due to the sheer size of the process state. A more feasible solutions is one where each node estimates a part of the global state vector, allowing different nodes in the network to have overlapping state elements. Although such an approach should be accompanied by a corresponding state fusion method, existing solutions cannot be employed as they merely consider fusion of two different estimates with equal state representations. Therefore, an empirical solution is presented for fusing two state estimates that have partially overlapping state elements. A justification of the proposed fusion method is presented, along with an illustrative case study for observing the temperature profile of a large rod, though a formal derivation is future research.
@inproceedings{ECC13_Sijs,
title = {{An Empirical Method to Fuse Partially Overlapping State Vectors for Distributed State Estimation}},
author = {Joris Sijs and Uwe D. Hanebeck and Benjamin Noack},
booktitle = {Proceedings of the 2013 European Control Conference (ECC 2013)},
address = {Z{\"u}rich, Switzerland},
doi = {10.23919/ECC.2013.6669738},
month = jul,
year = {2013}
}
Joris Sijs, Benjamin Noack, Uwe D. Hanebeck
Event-Based State Estimation with Negative Information Proceedings of the 16th International Conference on Information Fusion (Fusion 2013), Istanbul, Turkey, July, 2013.
To reduce the amount of data transfer in networked systems, measurements are usually taken only when an event occurs rather than periodically in time. However, this complicates estimation problems considerably as it is not guaranteed that new sensor data will be sampled. Therefore, an existing state estimator is extended so to cope with event-based measurements successfully, i.e., curtail any diverging behavior in the estimation results. To that extent, a general formulation of event sampling is proposed. This formulation is used to set up a state estimator combining stochastic as well as set-membership measurement information according to a hybrid update: when an event occurs the estimated state is updated using the stochastic measurement received (positive information), while at periodic time instants no measurement is received (negative information) and the update is based on knowledge that the sensor value lies within a bounded subset of the measurement space. An illustrative example further shows that the developed estimator has an improved representation of estimation errors compared to a purely stochastic estimator for various event sampling strategies.
@inproceedings{Fusion13_Sijs,
title = {{Event-Based State Estimation with Negative Information}},
author = {Joris Sijs and Benjamin Noack and Uwe D. Hanebeck},
booktitle = {Proceedings of the 16th International Conference on Information Fusion (Fusion 2013)},
address = {Istanbul, Turkey},
month = jul,
url = {https://ieeexplore.ieee.org/document/6641279},
year = {2013}
}
2012
Conferences
Benjamin Noack, Florian Pfaff, Uwe D. Hanebeck
Optimal Kalman Gains for Combined Stochastic and Set-Membership State Estimation Proceedings of the 51st IEEE Conference on Decision and Control (CDC 2012), Maui, Hawaii, USA, December, 2012.
In state estimation theory, two directions are mainly followed in order to model disturbances and errors. Either uncertainties are modeled as stochastic quantities or they are characterized by their membership to a set. Both approaches have distinct advantages and disadvantages making each one inherently better suited to model different sources of estimation uncertainty. This paper is dedicated to the task of combining stochastic and set-membership estimation methods. A Kalman gain is derived that minimizes the mean squared error in the presence of both stochastic and additional unknown but bounded uncertainties, which are represented by Gaussian random variables and ellipsoidal sets, respectively. As a result, a generalization of the well-known Kalman filtering scheme is attained that reduces to the standard Kalman filter in the absence of set-membership uncertainty and that otherwise becomes the intersection of sets in case of vanishing stochastic uncertainty. The proposed concept also allows to prioritize either the minimization of the stochastic uncertainty or the minimization of the set-membership uncertainty.
@inproceedings{CDC12_Noack,
title = {{Optimal Kalman Gains for Combined Stochastic and Set-Membership State Estimation}},
author = {Benjamin Noack and Florian Pfaff and Uwe D. Hanebeck},
booktitle = {Proceedings of the 51st IEEE Conference on Decision and Control (CDC 2012)},
address = {Maui, Hawaii, USA},
doi = {10.1109/CDC.2012.6426132},
month = dec,
year = {2012}
}
Marc Reinhardt, Benjamin Noack, Uwe D. Hanebeck
Decentralized Control Based on Globally Optimal Estimation Proceedings of the 51st IEEE Conference on Decision and Control (CDC 2012), Maui, Hawaii, USA, December, 2012.
A new method for globally optimal estimation in decentralized sensor-networks is applied to the decentralized control problem. The resulting approach is proven to be optimal when the nodes have access to all information in the network. More precisely, we utilize an algorithm for optimal distributed estimation in order to obtain local estimates whose combination yields the globally optimal estimate. When the interconnectivity is high, the local estimates are almost optimal, which motivates the application of the principle of separation. Thus, we optimize the controller and finally obtain a flexible algorithm, whose quality is evaluated in different scenarios. In applications where the strong requirements on a perfect communication cannot be guaranteed, we derive quality bounds by help of a detailed evaluation of the algorithm. When information is regularly exchanged, it is demonstrated that the algorithm performs almost optimally and therefore, offers system designers a flexible and easy to implement approach. The field of applications lies within the area of strongly networked systems, in particular, when communication disturbances cannot be foreseen or when the network structure is too complicated to apply optimized regulators.
@inproceedings{CDC12_Reinhardt,
title = {{Decentralized Control Based on Globally Optimal Estimation}},
author = {Marc Reinhardt and Benjamin Noack and Uwe D. Hanebeck},
booktitle = {Proceedings of the 51st IEEE Conference on Decision and Control (CDC 2012)},
address = {Maui, Hawaii, USA},
doi = {10.1109/CDC.2012.6426171},
month = dec,
year = {2012}
}
Marc Reinhardt, Benjamin Noack, Uwe D. Hanebeck
The Hypothesizing Distributed Kalman Filter Proceedings of the IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI 2012), Hamburg, Germany, September, 2012.
This paper deals with distributed information processing in sensor networks. We propose the Hypothesizing Distributed Kalman Filter that incorporates an assumption of the global measurement model into the distributed estimation process. The procedure is based on the Distributed Kalman Filter and inherits its optimality when the assumption about the global measurement uncertainty is met. Recursive formulas for local processing as well as for fusion are derived. We show that the proposed algorithm yields the same results, no matter whether the measurements are processed locally or globally, even when the process noise is not negligible. For further processing of the estimates, a consistent bound for the error covariance matrix is derived. All derivations and explanations are illustrated by means of a new classification scheme for estimation processes.
@inproceedings{MFI12_Reinhardt,
title = {{The Hypothesizing Distributed Kalman Filter}},
author = {Marc Reinhardt and Benjamin Noack and Uwe D. Hanebeck},
booktitle = {Proceedings of the IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI 2012)},
address = {Hamburg, Germany},
annote = {Nominee Best Student Paper Award},
doi = {10.1109/MFI.2012.6343017},
month = sep,
year = {2012}
}
Alessio Benavoli, Benjamin Noack
Pushing Kalman's Idea to the Extremes Proceedings of the 15th International Conference on Information Fusion (Fusion 2012), Singapore, July, 2012.
The paper focuses on the fundamental idea of Kalman’s seminal paper: how to solve the filtering problem from the only knowledge of the first two moments of the noise terms. In this paper, by exploiting set of distributions based filtering, we solve this problem without introducing additional assumptions on the distributions of the noise terms (e.g., Gaussianity) or on the final form of the estimator (e.g., linear estimator). Given the moments (e.g., mean and variance) of random variable X, it is possible to define the set of all distributions that are compatible with the moments information. This set of distributions can be equivalently characterized by its extreme distributions which is a family of mixtures of Dirac’s deltas. The lower and upper expectation of any function g of X are obtained in correspondence of these extremes and can be computed by solving a linear programming problem. The filtering problem can then be solved by running iteratively this linear programming problem.
@inproceedings{Fusion12_BenavoliNoack,
title = {{Pushing Kalman\textquotesingle s Idea to the Extremes}},
author = {Alessio Benavoli and Benjamin Noack},
booktitle = {Proceedings of the 15th International Conference on Information Fusion (Fusion 2012)},
address = {Singapore},
month = jul,
url = {https://ieeexplore.ieee.org/document/6289945},
year = {2012}
}
Benjamin Noack, Florian Pfaff, Uwe D. Hanebeck
Combined Stochastic and Set-membership Information Filtering in Multisensor Systems Proceedings of the 15th International Conference on Information Fusion (Fusion 2012), Singapore, July, 2012.
In state estimation theory, stochastic and set-membership approaches are generally considered separately from each other. Both concepts have distinct advantages and disadvantages making each one inherently better suited to model different sources of estimation uncertainty. In order to better utilize the potentials of both concepts, the core element of this paper is a Kalman filtering scheme that allows for a simultaneous treatment of stochastic and set-membership uncertainties. An uncertain quantity is herein modeled by a set of Gaussian densities. Since many modern applications operate in networked systems that may consist of a multitude of local processing units and sensor nodes, estimates have to be computed in a distributed manner and measurements may arrive at high frequency. An algebraic reformulation of the Kalman filter, the information filter, significantly eases the implementation of such distributed fusion architectures. This paper explicates how stochastic and set-membership uncertainties can simultaneously be treated within this information form and compared to the Kalman filter, it becomes apparent that the quality of some required approximations is enhanced.
@inproceedings{Fusion12_Noack,
title = {{Combined Stochastic and Set-membership Information Filtering in Multisensor Systems}},
author = {Benjamin Noack and Florian Pfaff and Uwe D. Hanebeck},
booktitle = {Proceedings of the 15th International Conference on Information Fusion (Fusion 2012)},
address = {Singapore},
month = jul,
url = {https://ieeexplore.ieee.org/document/6289947},
year = {2012}
}
Marc Reinhardt, Benjamin Noack, Uwe D. Hanebeck
On Optimal Distributed Kalman Filtering in Non-ideal Situations Proceedings of the 15th International Conference on Information Fusion (Fusion 2012), Singapore, July, 2012.
The distributed processing of measurements and the subsequent data fusion is called Track-to-Track fusion. Although a solution for the Track-to-Track fusion that is equivalent to a central processing scheme has been proposed, this algorithm suffers from strict requirements regarding the local availability of knowledge about utilized models of the remote nodes. By means of simple examples, we investigate the effects of incorrectly assumed models and trace the errors back to a bias, which we derive in closed form. We propose an extension to the exact Track-to-Track fusion algorithm that corrects the bias after arbitrarily many time steps. This new approach yields optimal results when the assumptions about the measurement models are correct and otherwise still provides the exact value for the mean-squared-error matrix. The performance of this algorithm is demonstrated and applications are presented that, e.g.,~allow the employment of nonlinear filter methods.
@inproceedings{Fusion12_Reinhardt,
title = {{On Optimal Distributed Kalman Filtering in Non-ideal Situations}},
author = {Marc Reinhardt and Benjamin Noack and Uwe D. Hanebeck},
booktitle = {Proceedings of the 15th International Conference on Information Fusion (Fusion 2012)},
address = {Singapore},
month = jul,
url = {https://ieeexplore.ieee.org/document/6289921},
year = {2012}
}
Marc Reinhardt, Benjamin Noack, Uwe D. Hanebeck
Closed-form Optimization of Covariance Intersection for Low-dimensional Matrices Proceedings of the 15th International Conference on Information Fusion (Fusion 2012), Singapore, July, 2012.
The fusion under unknown correlations is an important technique in sensor-network information processing as the cross-correlations between different estimates remain often unknown to the nodes. Covariance intersection is a wide-spread and efficient algorithm to fuse estimates under such uncertain conditions. Although different optimization criteria have been developed, the trace or determinant minimization of the fused covariance matrix seems to be most meaningful. However, this minimization requires numeric solutions of a convex optimization problem. We derive an algorithm to reduce this nonlinear optimization to the well-known polynomial root-finding problem. This allows us to present closed-form solutions for the determinant criterion when the dimension of the occurring covariance matrices is at most~4 and for the trace criterion when the dimension of the covariance matrices is at most~3. We demonstrate the effectiveness of the approach by means of a speed evaluation.
@inproceedings{Fusion12_Reinhardt-FastCI,
title = {{Closed-form Optimization of Covariance Intersection for Low-dimensional Matrices}},
author = {Marc Reinhardt and Benjamin Noack and Uwe D. Hanebeck},
booktitle = {Proceedings of the 15th International Conference on Information Fusion (Fusion 2012)},
address = {Singapore},
month = jul,
url = {https://ieeexplore.ieee.org/document/6290531},
year = {2012}
}
2011
Conferences
Marcus Baum, Benjamin Noack, Uwe D. Hanebeck
Mixture Random Hypersurface Models for Tracking Multiple Extended Objects Proceedings of the 50th IEEE Conference on Decision and Control (CDC 2011), Orlando, Florida, USA, December, 2011.
This paper presents a novel method for tracking multiple extended objects. The shape of a single extended object is modeled with a recently developed approach called Random Hypersurface Model (RHM) that assumes a varying number of measurement sources to lie on scaled versions of the shape boundaries. This approach is extended by introducing a so-called Mixture Random Hypersurface Model (Mixture RHM), which allows for modeling multiple extended targets. Based on this model, a Gaussian-assumed Bayesian tracking method that provides the means to track and estimate shapes of multiple extended targets is derived. Simulations demonstrate the performance of the new approach.
@inproceedings{CDC11_Baum,
title = {{Mixture Random Hypersurface Models for Tracking Multiple Extended Objects}},
author = {Marcus Baum and Benjamin Noack and Uwe D. Hanebeck},
booktitle = {Proceedings of the 50th IEEE Conference on Decision and Control (CDC 2011)},
address = {Orlando, Florida, USA},
doi = {10.1109/CDC.2011.6161522},
month = dec,
year = {2011}
}
Benjamin Noack, Marcus Baum, Uwe D. Hanebeck
Automatic Exploitation of Independencies for Covariance Bounding in Fully Decentralized Estimation Proceedings of the 18th IFAC World Congress (IFAC 2011), Milan, Italy, August, 2011.
Especially in the field of sensor networks and multi-robot systems, fully decentralized estimation techniques are of particular interest. As the required elimination of the complex dependencies between estimates generally yields inconsistent results, several approaches, e.g., covariance intersection, maintain consistency by providing conservative estimates. Unfortunately, these estimates are often too conservative and therefore, much less informative than a corresponding centralized approach. In this paper, we provide a concept that conservatively decorrelates the estimates while bounding the unknown correlations as closely as possible. For this purpose, known independent quantities, such as measurement noise, are explicitly identified and exploited. Based on tight covariance bounds, the new approach allows for an intuitive and systematic derivation of appropriate tailor-made filter equations and does not require heuristics. Its performance is demonstrated in a comparative study within a typical SLAM scenario.
@inproceedings{IFAC11_Noack,
title = {{Automatic Exploitation of Independencies for Covariance Bounding in Fully Decentralized Estimation}},
author = {Benjamin Noack and Marcus Baum and Uwe D. Hanebeck},
booktitle = {Proceedings of the 18th IFAC World Congress (IFAC 2011)},
address = {Milan, Italy},
doi = {10.3182/20110828-6-IT-1002.03524},
month = aug,
year = {2011}
}
Marcus Baum, Benjamin Noack, Frederik Beutler, Dominik Itte, Uwe D. Hanebeck
Optimal Gaussian Filtering for Polynomial Systems Applied to Association-free Multi-Target Tracking Proceedings of the 14th International Conference on Information Fusion (Fusion 2011), Chicago, Illinois, USA, July, 2011.
This paper is about tracking multiple targets with the so-called Symmetric Measurement Equation (SME) filter. The SME filter uses symmetric functions, e.g., symmetric polynomials, in order to remove the data association uncertainty from the measurement equation. By this means, the data association problem is converted to a nonlinear state estimation problem. In this work, an efficient optimal Gaussian filter based on analytic moment calculation for discrete-time multi-dimensional polynomial systems corrupted with Gaussian noise is derived, and then applied to the polynomial system resulting from the SME filter. The performance of the new method is compared to an UKF implementation by means of typical multiple target tracking scenarios.
@inproceedings{Fusion11_Baum,
title = {{Optimal Gaussian Filtering for Polynomial Systems Applied to Association-free Multi-Target Tracking}},
author = {Marcus Baum and Benjamin Noack and Frederik Beutler and Dominik Itte and Uwe D. Hanebeck},
booktitle = {Proceedings of the 14th International Conference on Information Fusion (Fusion 2011)},
address = {Chicago, Illinois, USA},
month = jul,
url = {https://ieeexplore.ieee.org/document/5977706},
year = {2011}
}
Benjamin Noack, Marcus Baum, Uwe D. Hanebeck
Covariance Intersection in Nonlinear Estimation Based on Pseudo Gaussian Densities Proceedings of the 14th International Conference on Information Fusion (Fusion 2011), Chicago, Illinois, USA, July, 2011.
Many modern fusion architectures are designed to process and fuse data in networked systems. Alongside the advantages, such as scalability and robustness, distributed fusion techniques particularly have to tackle the problem of dependencies between locally processed data. In linear estimation problems, uncertain quantities with unknown cross-correlations can be fused by means of the covariance intersection algorithm, which avoids overconfident fusion results. However, for nonlinear system dynamics and sensor models perturbed by arbitrary noise, it is not only a problem to characterize and parameterize dependencies between estimates, but also to find a proper notion of consistency. This paper addresses these issues by transforming the state estimates to a different state space, where the corresponding densities are Gaussian and only linear dependencies between estimates, i.e., correlations, can arise. These pseudo Gaussian densities then allow the notion of covariance consistency to be used in distributed nonlinear state estimation.
@inproceedings{Fusion11_Noack,
title = {{Covariance Intersection in Nonlinear Estimation Based on Pseudo Gaussian Densities}},
author = {Benjamin Noack and Marcus Baum and Uwe D. Hanebeck},
booktitle = {Proceedings of the 14th International Conference on Information Fusion (Fusion 2011)},
address = {Chicago, Illinois, USA},
month = jul,
url = {https://ieeexplore.ieee.org/document/5977577},
year = {2011}
}
Marc Reinhardt, Benjamin Noack, Marcus Baum, Uwe D. Hanebeck
Analysis of Set-theoretic and Stochastic Models for Fusion under Unknown Correlations Proceedings of the 14th International Conference on Information Fusion (Fusion 2011), Chicago, Illinois, USA, July, 2011.
In data fusion theory, multiple estimates are combined to yield an optimal result. In this paper, the set of all possible results is investigated, when two random variables with unknown correlations are fused. As a first step, recursive processing of the set of estimates is examined. Besides set-theoretic considerations, the lack of knowledge about the unknown correlation coefficient is modeled as a stochastic quantity. Especially, a uniform model is analyzed, which provides a new optimization criterion for the covariance intersection algorithm in scalar state spaces. This approach is also generalized to multi-dimensional state spaces in an approximative, but fast and scalable way, so that consistent estimates are obtained.
@inproceedings{Fusion11_Reinhardt,
title = {{Analysis of Set-theoretic and Stochastic Models for Fusion under Unknown Correlations}},
author = {Marc Reinhardt and Benjamin Noack and Marcus Baum and Uwe D. Hanebeck},
booktitle = {Proceedings of the 14th International Conference on Information Fusion (Fusion 2011)},
address = {Chicago, Illinois, USA},
month = jul,
url = {https://ieeexplore.ieee.org/document/5977580},
year = {2011}
}
Benjamin Noack, Daniel Lyons, Matthias Nagel, Uwe D. Hanebeck
Nonlinear Information Filtering for Distributed Multisensor Data Fusion Proceedings of the 2011 American Control Conference (ACC 2011), San Francisco, California, USA, June, 2011.
The information filter has evolved into a key tool for distributed and decentralized multisensor estimation and control. Essentially, it is an algebraical reformulation of the Kalman filter and provides estimates on the information about an uncertain state rather than on a state itself. Whereas many practicable Kalman filtering techniques for nonlinear system and sensor models have been developed, approaches towards nonlinear information filtering are still scarce and limited. In order to deal with nonlinear systems and sensors, this paper derives an approximation technique for arbitrary probability densities that provides the same distributable fusion structure as the linear information filter. The presented approach not only constitutes a nonlinear version of the information filter, but it also points the direction to a Hilbert space structure on probability densities, whose vector space operations correspond to the fusion and weighting of information.
@inproceedings{ACC11_Noack,
title = {{Nonlinear Information Filtering for Distributed Multisensor Data Fusion}},
author = {Benjamin Noack and Daniel Lyons and Matthias Nagel and Uwe D. Hanebeck},
booktitle = {Proceedings of the 2011 American Control Conference (ACC 2011)},
address = {San Francisco, California, USA},
doi = {10.1109/ACC.2011.5991535},
month = jun,
year = {2011}
}
Johannes Schmid, Frederik Beutler, Benjamin Noack, Uwe D. Hanebeck, Klaus D. Müller-Glaser
An Experimental Evaluation of Position Estimation Methods for Person Localization in Wireless Sensor Networks Proceedings of the 8th European Conference on Wireless Sensor Networks (EWSN 2011), vol. 6567, pp. 147–162, Springer, Bonn, Germany, February, 2011.
In this paper, the localization of persons by means of a Wireless Sensor Network (WSN) is considered. Persons carry on-body sensor
nodes and move within a WSN. The location of each person is calculated
on this node and communicated through the network to a central data
sink for visualization. Applications of such a system could be found in
mass casualty events, firefighter scenarios, hospitals or retirement homes for example.
For the location estimation on the sensor node, three derivatives of the
Kalman Filter and a closed-form solution (CFS) are applied, compared,
and evaluated in a real-world scenario. A prototype 65-node ZigBee WSN
is implemented and data are collected in in- and outdoor environments
with differently positioned on-body nodes. The described estimators are
then evaluated off-line on the experimentally collected data.
The goal of this paper is to present a comprehensive real-world evaluation of methods for
person localization in a WSN based on received signal strength (RSS) range measurements.
It is concluded that person localization in in- and outdoor environments is possible
under the considered conditions with the considered filters. The compared methods
allow for suffciently accurate localization results and are robust against
inaccurate range measurements.
@inproceedings{EWSN11_Schmid,
title = {{An Experimental Evaluation of Position Estimation Methods for Person Localization in Wireless Sensor Networks}},
author = {Johannes Schmid and Frederik Beutler and Benjamin Noack and Uwe D. Hanebeck and Klaus D. M{\"u}ller-Glaser},
booktitle = {Proceedings of the 8th European Conference on Wireless Sensor Networks (EWSN 2011)},
address = {Bonn, Germany},
doi = {10.1007/978-3-642-19186-2_10},
editor = {Pedro José Marrón and Kamin Whitehouse},
month = feb,
pages = {147--162},
publisher = {Springer},
volume = {6567},
year = {2011}
}
2010
Book Chapters
Daniel Lyons, Achim Hekler, Benjamin Noack, Uwe D. Hanebeck
Maße für Wahrscheinlichkeitsdichten in der informationstheoretischen Sensoreinsatzplanung Verteilte Messsysteme, pp. 121–132, KIT Scientific Publishing, March, 2010.
Bei der Beobachtung eines räumlich verteilten Phänomens mit einer
Vielzahl von Sensoren ist die intelligente Auswahl von Messkonfigurationen aufgrund von
beschränkten Rechen- und Kommunikationskapazitäten entscheidend für die
Lebensdauer des Sensornetzes. Mit der Sensoreinsatzplanung kann die im nächsten
Zeitschritt anzusteuernde Messkonfiguration dynamisch mittels einer stochastischen
modell-prädiktiven Planung über einen endlichen Zeithorizont bestimmt werden.
Dabei wird als Gütekriterium die Maximierung des zu erwartenden Informationsgewinns
durch zukünftige Messungen unter sparsamer Verwendung der Energieressourcen gewählt.
In diesem Artikel wird ein neues Maß für kontinuierliche Wahrscheinlichkeitsdichten
vorgestellt, das sich kanonisch aus der Konstruktion eines Vektorraums für
Wahrscheinlichkeitsdichten ergibt. Dieses Maß wird als Gütefunktion in der
vorausschauenden Sensoreinsatzplanung zur Bewertung des informationstheoretischen Einfluß
von Messungen auf die aktuelle Zustandsschätzung verwendet.
@incollection{VMS10_Lyons,
title = {{Ma{\ss}e f{\"u}r Wahrscheinlichkeitsdichten in der informationstheoretischen Sensoreinsatzplanung}},
author = {Daniel Lyons and Achim Hekler and Benjamin Noack and Uwe D. Hanebeck},
booktitle = {Verteilte Messsysteme},
doi = {10.5445/KSP/1000015670},
editor = {Fernando Puente León and Klaus-Dieter Sommer and Michael Heizmann},
month = mar,
pages = {121--132},
publisher = {KIT Scientific Publishing},
url = {http://digbib.ubka.uni-karlsruhe.de/volltexte/1000015670},
year = {2010}
}
Benjamin Noack, Vesa Klumpp, Daniel Lyons, Uwe D. Hanebeck
Systematische Beschreibung von Unsicherheiten in der Informationsfusion mit Mengen von Wahrscheinlichkeitsdichten Verteilte Messsysteme, pp. 167–178, KIT Scientific Publishing, March, 2010.
Die systematische Behandlung von Unsicherheiten stellt eine wesentliche
Herausforderung in der Informationsfusion dar. Einerseits müssen geeignete Darstellungsformen
für die Unsicherheiten bestimmt werden und andererseits darauf aufbauend effiziente
Schätzverfahren hergeleitet werden. Im Allgemeinen wird zwischen stochastischen und
mengenbasierten Unsicherheitsbeschreibungen unterschieden. Dieser Beitrag stellt ein Verfahren
zur Zustandsschätzung vor, welches simultan stochastische und mengenbasierte Fehlergrößen
berücksichtigen kann, indem unsichere Größen nicht mehr durch eine einzelne
Wahrscheinlichkeitsdichte, sondern durch eine Menge von Dichten repräsentiert werden.
Besonderes Augenmerk liegt hier auf den Vorteilen und Anwendungsmöglichkeiten dieser
Unsicherheitsbeschreibung.
@incollection{VMS10_Noack,
title = {{Systematische Beschreibung von Unsicherheiten in der Informationsfusion mit Mengen von Wahrscheinlichkeitsdichten}},
author = {Benjamin Noack and Vesa Klumpp and Daniel Lyons and Uwe D. Hanebeck},
booktitle = {Verteilte Messsysteme},
editor = {Fernando Puente León and Klaus-Dieter Sommer and Michael Heizmann},
month = mar,
pages = {167--178},
publisher = {KIT Scientific Publishing},
url = {http://digbib.ubka.uni-karlsruhe.de/volltexte/1000015670},
year = {2010}
}
Journal Articles
Benjamin Noack, Vesa Klumpp, Daniel Lyons, Uwe D. Hanebeck
Modellierung von Unsicherheiten und Zustandsschätzung mit Mengen von Wahrscheinlichkeitsdichten tm - Technisches Messen, Oldenbourg Verlag, vol. 77, no. 10, pp. 544–550, October, 2010.
Die systematische Behandlung von Unsicherheiten stellt eine wesentliche Herausforderung in der Informationsfusion dar. Einerseits müssen geeignete Darstellungsformen für die Unsicherheiten bestimmt werden und andererseits darauf aufbauend effiziente Schätzverfahren hergeleitet werden. Im Allgemeinen wird zwischen stochastischen und mengenbasierten Unsicherheitsbeschreibungen unterschieden. Dieser Beitrag stellt ein Verfahren zur Zustandsschätzung vor, welches simultan stochastische und mengenbasierte Fehlergrößen berücksichtigen kann, indem unsichere Größen nicht mehr durch eine einzelne Wahrscheinlichkeitsdichte, sondern durch eine Menge von Dichten repräsentiert werden. Besonderes Augenmerk liegt hier auf den Vorteilen und Anwendungsmöglichkeiten dieser Unsicherheitsbeschreibung.
@article{TM10_Noack,
title = {{Modellierung von Unsicherheiten und Zustandssch{\"a}tzung mit Mengen von Wahrscheinlichkeitsdichten}},
author = {Benjamin Noack and Vesa Klumpp and Daniel Lyons and Uwe D. Hanebeck},
doi = {10.1524/teme.2010.0087},
editor = {Klaus-Dieter Sommer and Fernando Puente León and Michael Heizmann},
journal = {tm - Technisches Messen, Oldenbourg Verlag},
month = oct,
number = {10},
pages = {544--550},
volume = {77},
year = {2010}
}
Conferences
Evgeniya Bogatyrenko, Benjamin Noack, Uwe D. Hanebeck
Reliable Estimation of Heart Surface Motion under Stochastic and Unknown but Bounded Systematic Uncertainties Proceedings of the 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2010), Taipei, Taiwan, October, 2010.
A reliable estimation of heart surface motion
is an important prerequisite for the synchronization of surgical
instruments in robotic beating heart surgery. In general, only
an imprecise description of the heart dynamics and measurement
systems is available. This means that the estimation of heart
motion is corrupted by stochastic and systematic uncertainties.
Without consideration of these uncertainties, the obtained results
will be inaccurate and a safe robotic operation cannot be guaranteed.
Until now, existing approaches for estimating the motion of the
heart surface are either deterministic or treat only stochastic
uncertainties. The proposed method extends the heart motion
estimation to the simultaneous consideration of stochastic and
unknown but bounded systematic uncertainties. It computes dynamic
bounds in order to provide the surgeon with a guidance by
constraining the motion of the surgical instruments and thereby
protecting sensitive tissue.
@inproceedings{IROS10_Bogatyrenko,
title = {{Reliable Estimation of Heart Surface Motion under Stochastic and Unknown but Bounded Systematic Uncertainties}},
author = {Evgeniya Bogatyrenko and Benjamin Noack and Uwe D. Hanebeck},
booktitle = {Proceedings of the 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2010)},
address = {Taipei, Taiwan},
doi = {10.1109/IROS.2010.5651190},
month = oct,
year = {2010}
}
Achim Hekler, Daniel Lyons, Benjamin Noack, Uwe D. Hanebeck
Nonlinear Model Predictive Control Considering Stochastic and Systematic Uncertainties with Sets of Densities Proceedings of the IEEE Multi-Conference on Systems and Control (MSC 2010), Yokohama, Japan, September, 2010.
In Model Predictive Control, the quality of control
is highly dependent upon the model of the system under control.
Therefore, a precise deterministic model is desirable. However,
in real-world applications, modeling accuracy is typically limited
and systems are generally affected by disturbances. Hence,
it is important to systematically consider these uncertainties
and to model them correctly. In this paper, we present a
novel Nonlinear Model Predictive Control method for systems
affected by two different types of perturbations that are
modeled as being either stochastic or unknown but bounded
quantities. We derive a formal generalization of the Nonlinear
Model Predictive Control principle for considering both types
of uncertainties simultaneously, which is achieved by using
sets of probability densities. In doing so, a more robust and
reliable control is obtained. The capabilities and benefits of
our approach are demonstrated in real-world experiments with
miniature walking robots.
@inproceedings{MSC10_HeklerLyonsNoack,
title = {{Nonlinear Model Predictive Control Considering Stochastic and Systematic Uncertainties with Sets of Densities}},
author = {Achim Hekler and Daniel Lyons and Benjamin Noack and Uwe D. Hanebeck},
booktitle = {Proceedings of the IEEE Multi-Conference on Systems and Control (MSC 2010)},
address = {Yokohama, Japan},
doi = {10.1109/CCA.2010.56112417},
month = sep,
year = {2010}
}
Marcus Baum, Benjamin Noack, Uwe D. Hanebeck
Extended Object and Group Tracking with Elliptic Random Hypersurface Models Proceedings of the 13th International Conference on Information Fusion (Fusion 2010), Edinburgh, United Kingdom, July, 2010.
This paper provides new results and
insights for tracking an extended target object
modeled with an Elliptic Random Hypersurface Model (RHM).
An Elliptic RHM specifies the relative squared Mahalanobis
distance of a measurement source to the center of the
target object by means of a one-dimensional random scaling
factor. It is shown that uniformly distributed measurement
sources on an ellipse lead to a uniformly distributed
squared scaling factor. Furthermore, a Bayesian inference
mechanisms tailored to elliptic shapes is introduced, which
is also suitable for scenarios with high measurement noise.
Closed-form expressions for the measurement update in case
of Gaussian and uniformly distributed squared scaling factors are derived.
@inproceedings{Fusion10_BaumNoack,
title = {{Extended Object and Group Tracking with Elliptic Random Hypersurface Models}},
author = {Marcus Baum and Benjamin Noack and Uwe D. Hanebeck},
booktitle = {Proceedings of the 13th International Conference on Information Fusion (Fusion 2010)},
address = {Edinburgh, United Kingdom},
doi = {10.1109/ICIF.2010.5711854},
month = jul,
year = {2010}
}
Vesa Klumpp, Benjamin Noack, Marcus Baum, Uwe D. Hanebeck
Combined Set-Theoretic and Stochastic Estimation: A Comparison of the SSI and the CS Filter Proceedings of the 13th International Conference on Information Fusion (Fusion 2010), Edinburgh, United Kingdom, July, 2010.
In estimation theory, mainly set-theoretic or
stochastic uncertainty is considered. In some cases, especially when
some statistics of a distribution are not known or additional
stochastic information is used in a set-theoretic estimator, both
types of uncertainty have to be considered. In this paper, two
estimators that cope with combined stoachastic and set-theoretic
uncertainty are compared, namely the Set-theoretic and Statistical
Information filter, which represents the uncertainty by means of
random sets, and the Credal State filter, in which the state
information is given by sets of probability density functions.
The different uncertainty assessment in both estimators leads to
different estimation results, even when the prior information and
the measurement and system models are equal. This paper explains
these differences and states directions, when which estimator
should be applied to a given estimation problem.
@inproceedings{Fusion10_Klumpp,
title = {{Combined Set-Theoretic and Stochastic Estimation: A Comparison of the SSI and the CS Filter}},
author = {Vesa Klumpp and Benjamin Noack and Marcus Baum and Uwe D. Hanebeck},
booktitle = {Proceedings of the 13th International Conference on Information Fusion (Fusion 2010)},
address = {Edinburgh, United Kingdom},
doi = {10.1109/ICIF.2010.5711908},
month = jul,
year = {2010}
}
Benjamin Noack, Vesa Klumpp, Nikolay Petkov, Uwe D. Hanebeck
Bounding Linearization Errors with Sets of Densities in Approximate Kalman Filtering Proceedings of the 13th International Conference on Information Fusion (Fusion 2010), Edinburgh, United Kingdom, July, 2010.
Applying the Kalman filtering scheme to linearized system dynamics and observation models does in general not yield optimal state estimates.
More precisely, inconsistent state estimates and covariance matrices are caused by neglected linearization errors.
This paper introduces a concept for systematically predicting and updating bounds for the linearization errors within the Kalman filtering framework.
To achieve this, an uncertain quantity is not characterized by a single probability density anymore, but rather by a set of densities and accordingly,
the linear estimation framework is generalized in order to process sets of probability densities. By means of this generalization,
the Kalman filter may then not only be applied to stochastic quantities, but also to unknown but bounded quantities.
In order to improve the reliability of Kalman filtering results, the last-mentioned quantities are utilized to bound the typically neglected nonlinear parts of a linearized mapping.
@inproceedings{Fusion10_Noack,
title = {{Bounding Linearization Errors with Sets of Densities in Approximate Kalman Filtering}},
author = {Benjamin Noack and Vesa Klumpp and Nikolay Petkov and Uwe D. Hanebeck},
booktitle = {Proceedings of the 13th International Conference on Information Fusion (Fusion 2010)},
address = {Edinburgh, United Kingdom},
doi = {10.1109/ICIF.2010.5711909},
month = jul,
year = {2010}
}
Daniel Lyons, Benjamin Noack, Uwe D. Hanebeck
A Log-Ratio Information Measure for Stochastic Sensor Management Proceedings of the IEEE International Conference on Sensor Networks, Ubiquitous, and Trustworthy Computing (SUTC 2010), Newport Beach, California, USA, June, 2010.
In distributed sensor networks, computational and energy resources are
in general limited. Therefore, an intelligent selection of sensors for
measurements is of great importance to ensure both high estimation
quality and an extended lifetime of the network. Methods from the theory
of model predictive control together with information theoretic measures
have been employed to pick sensors yielding measurements with high
information value. We present a novel information measure that originates from a
scalar product on a class of continuous probability densities and apply it
to the field of sensor management. Aside from its mathematical justifications
for quantifying the information content of probability densities, the most
remarkable property of the measure, an analogon of the triangle inequality
under Bayesian information fusion, is deduced. This allows for deriving
computationally cheap upper bounds for the model predictive sensor selection
algorithm and for comparing the performance of planning over different lengths of time horizons.
@inproceedings{SUTC10_Lyons,
title = {{A Log-Ratio Information Measure for Stochastic Sensor Management}},
author = {Daniel Lyons and Benjamin Noack and Uwe D. Hanebeck},
booktitle = {Proceedings of the IEEE International Conference on Sensor Networks, Ubiquitous, and Trustworthy Computing (SUTC 2010)},
address = {Newport Beach, California, USA},
doi = {10.1109/SUTC.2010.48},
month = jun,
year = {2010}
}
2009
Conferences
Benjamin Noack, Vesa Klumpp, Uwe D. Hanebeck
State Estimation with Sets of Densities considering Stochastic and Systematic Errors Proceedings of the 12th International Conference on Information Fusion (Fusion 2009), Seattle, Washington, USA, July, 2009.
In practical applications, state estimation requires the consideration of
stochastic and systematic errors. If both error types are present, an exact
probabilistic description of the state estimate is not possible, so that
common Bayesian estimators have to be questioned. This paper introduces a
theoretical concept, which allows for incorporating unknown but bounded errors
into a Bayesian inference scheme by utilizing sets of densities. In order to
derive a tractable estimator, the Kalman filter is applied to ellipsoidal sets
of means, which are used to bound additive systematic errors. Also, an
extension to nonlinear system and observation models with ellipsoidal error
bounds is presented. The derived estimator is motivated by means of two
example applications.
@inproceedings{Fusion09_Noack,
title = {{State Estimation with Sets of Densities considering Stochastic and Systematic Errors}},
author = {Benjamin Noack and Vesa Klumpp and Uwe D. Hanebeck},
booktitle = {Proceedings of the 12th International Conference on Information Fusion (Fusion 2009)},
address = {Seattle, Washington, USA},
month = jul,
url = {https://ieeexplore.ieee.org/document/5203820},
year = {2009}
}
2008
Conferences
Benjamin Noack, Vesa Klumpp, Dietrich Brunn, Uwe D. Hanebeck
Nonlinear Bayesian Estimation with Convex Sets of Probability Densities Proceedings of the 11th International Conference on Information Fusion (Fusion 2008), Cologne, Germany, July, 2008.
This paper presents a theoretical framework for
Bayesian estimation in the case of imprecisely known probability
density functions. The lack of knowledge about the true density
functions is represented by sets of densities. A formal Bayesian
estimator for these sets is introduced, which is intractable for
infinite sets. To obtain a tractable filter, properties of convex
sets in form of convex polytopes of densities are investigated.
It is shown that pathwise connected sets and their convex hulls
describe the same ignorance. Thus, an exact algorithm is derived,
which only needs to process the hull, delivering tractable results
in the case of a proper parametrization. Since the estimator
delivers a convex hull of densities as output, the theoretical
grounds are laid for deriving efficient Bayesian estimators for
sets of densities. The derived filter is illustrated by means of an
example.
@inproceedings{Fusion08_Noack-ConvexSets,
title = {{Nonlinear Bayesian Estimation with Convex Sets of Probability Densities}},
author = {Benjamin Noack and Vesa Klumpp and Dietrich Brunn and Uwe D. Hanebeck},
booktitle = {Proceedings of the 11th International Conference on Information Fusion (Fusion 2008)},
address = {Cologne, Germany},
month = jul,
url = {https://ieeexplore.ieee.org/document/4632189},
year = {2008}
}
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