Cooperative Approaches to Design of Nonlinear Filters
Final Report Abstract
In this project, we focused on the combination of state estimates to design cooperative filters. We investigated and further developed two compelling previously proposed methods to reconstruct cross-covariances for achieving an optimal fusion of state estimates. The first method utilized deterministic samples, while the second used square-root decompositions of dependent information. Both methods are based on the same underlying principle for the linear fusion of state estimates and can be used interchangeably. However, we found that the square-root decomposition is slightly more intuitive and easier to use while also requiring fewer data to be communicated. On the other hand, sample-based reconstruction could be better suited to nonlinear combinations of state estimates. During this project, we addressed some initial problems of the sample-based reconstruction of cross-covariances. A drawback of the method’s initial design was the fixed time horizon until the fusion had to be executed. This time horizon can now be determined in a flexible way because samples are created on the go. Further, we proposed to approximate nonlinear system models by a linear transformation matrix. Last, we discussed approaches to keep the number of samples within the sample set constant to reduce bandwidth requirements. A limitation of both approaches was the relatively narrow application to the combination of estimates on only one dedicated fusion center. While this is a common scenario for many sensor networks, there are applications where several fusion centers exist, and that require more careful consideration. Therefore, a significant contribution was made by generalizing the square-root decomposition to networks with several consecutive fusion steps, e.g., tree topologies and fully decentralized sensor networks, e.g., net topologies. This generalization makes it possible to calculate the exact cross-covariances even in complicated network topologies, filling a critical literature gap. Further, we proposed several approaches to address limited bandwidth by partial reconstruction of cross-covariances and bounding of remaining possibly correlated information. This work has won the best paper award at the 23rd Conference on Information Fusion (Fusion) in 2020. We also investigated the combination of heterogeneous state estimates that either overlap at certain state estimates or refer to state estimates from different coordinate systems. We showed that cross-covariances between overlapping state estimates can be calculated and used to improve the fusion result. Our research also showed that the separation of global phenomena into smaller subproblems needs special care to model uncertainties, and several open research questions remain. When combining state estimates from different coordinate systems that are subject to linear transformations, we showed that an optimal combination is possible even when the dimension of the system state is reduced. We also found that this does not hold when considering nonlinear transformations because reducing the state dimension will lead to underestimating process uncertainties. Our research discovered many open questions concerning the nonlinear combination of state estimates requiring further investigation in a follow-up examination.
Publications
- Reconstruction of Cross-Correlations with Constant Number of Deterministic Samples. In Proceedings of the 21st International Conference on Information Fusion (Fusion 2018), Cambridge, United Kingdom, July 2018
Radtke, Susanne, Benjamin Noack, Uwe D. Hanebeck and Ondrej Straka
(See online at https://doi.org/10.23919/ICIF.2018.8455221) - Comparative Study of Track-to-Track Fusion Methods for Cooperative Tracking with Bearings-only Measurements. In Proceedings of the 2019 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI 2019), Taipei, Republic of China, May 2019
Radtke, Susanne, Kailai Li, Benjamin Noack and Uwe D. Hanebeck
(See online at https://doi.org/10.1109/ICPHYS.2019.8780330) - Distributed Estimation using Square Root Decompositions of Dependent Information. In Proceedings of the 22nd International Conference on Information Fusion (Fusion 2019), Ottawa, Canada, July 2019
Radtke, Susanne, Benjamin Noack and Uwe D. Hanebeck
- Distributed Estimation with Partially Overlapping States based on Deterministic Samplebased Fusion. In Proceedings of the 2019 European Control Conference (ECC 2019), Naples, Italy, June 2019
Radtke, Susanne, Benjamin Noack and Uwe D. Hanebeck
(See online at https://doi.org/10.23919/ECC.2019.8795853) - Fully Decentralized Estimation Using Square-Root Decompositions. In Proceedings of the 23rd International Conference on Information Fusion (Fusion 2020), Virtual, July 2020
Radtke, Susanne, Benjamin Noack and Uwe D. Hanebeck
(See online at https://doi.org/10.23919/FUSION45008.2020.9190294) - Reconstruction of Cross-Correlations between Heterogeneous Trackers Using Deterministic Samples. In Proceedings of the 1st Virtual IFAC World Congress (IFAC-V 2020), July 2020
Radtke, Susanne, Benjamin Noack and Uwe D. Hanebeck
(See online at https://doi.org/10.5445/IR/1000121278)
