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Dynamic rEvolution: Adaptive state estimation via Gaussian processes and iterative filtering
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-0572-2665
2024 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

For virtually every area of science and engineering, state estimation is ubiquitous. Accurate state estimation requires a moderately precise mathematical model of the system, typically based on domain expertise. These models exist for a plethora of applications and available state estimators can generally produce accurate estimates. However, the models usually ignore hard-to-model phenomena, either due to the cost or the difficulty of modeling these characteristics. Further, the most widely used state estimator for nonlinear systems is still the extended Kalman filter (EKF), which may suffer from divergence for complex models, which essentially restricts the complexity of the usable models. Generally speaking, this thesis investigates ways of improving state estimation. Firstly, existing state-space models (SSMs) for target tracking are augmented with a Gaussian process (GP) in order to learn hard-to-model system characteristics online. Secondly, improved linearization-based state estimators are proposed that exhibit favorable robustness properties to the parameters of the noise processes driving the SSM.

The first part of the thesis explores joint state estimation and model learning in partially unknown SSMs, where some a priori domain expertise is available, but parts of the model need to be learned online. Paper A combines a linear, a priori identified, SSM with an approximate GP. An EKF is applied to this GP-augmented SSM in order to jointly estimate the state of the system and learn the, a priori, unknown dynamics. This empirically works well and substantially reduces the prediction error of the dynamical model as compared to a non-augmented SSM. Paper B explores ways of reducing the computational complexity of the method of Paper A. Crucially, it uses a compact kernel in the GP, which admits an equivalent basis function (BF) representation where only a few BFs are non-zero at any given system state. This enables a method that is essentially computationally invariant to the number of parameters, where the computational complexity can be tuned by hyperparameters of the BFs.

The second part explores iterated filters as a means to increase robustness to improper noise parameter choices. As the nonlinearities in the model are mainly contained in the dynamics, standard iterated filters such as the iterated extended Kalman filter (IEKF) can not be used. Papers C and D develop dynamically iterated filters (DIFs), which is a unified framework for linearization-based iterated filters that deal with nonlinearities in both the dynamics as well as the measurement model. The DIFs are shown to be robust toward improper noise parameter tuning and improve the mean square error (MSE) as compared to their corresponding non-iterated baselines.

The third and final part of the thesis considers an alternative bf representation of the GP model, the Hilbert-space Gaussian process (HGP), which is essentially a sinusoidal representation on a compact domain. Paper E identifies previously unutilized Hankel-Toeplitz structure in the HGP, which enables a time complexity for learning that is linear in the number of BFs, without further approximation. Lastly, Paper F improves the computational complexity of prediction in the HGP, by adaptively choosing the most important BFs for prediction in a certain region of the input.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2024. , p. 67
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 2391
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:liu:diva-203428DOI: 10.3384/9789180756747ISBN: 9789180756730 (print)ISBN: 9789180756747 (electronic)OAI: oai:DiVA.org:liu-203428DiVA, id: diva2:1857333
Public defence
2024-06-14, BL32 (Nobel), B Building, Campus Valla, Linköping, 09:30 (English)
Opponent
Supervisors
Note

Funding agency: The Wallenberg AI and Autonomous Systems and Software Program (WASP), funded by the Knut and Alice Wallenberg Foundation

Available from: 2024-05-13 Created: 2024-05-13 Last updated: 2024-05-14Bibliographically approved
List of papers
1. Learning Driver Behaviors Using A Gaussian Process Augmented State-Space Model
Open this publication in new window or tab >>Learning Driver Behaviors Using A Gaussian Process Augmented State-Space Model
2020 (English)In: Proceedings of 2020 23rd International Conference on Information Fusion (FUSION 2020), Institute of Electrical and Electronics Engineers (IEEE), 2020, p. 530-536Conference paper, Published paper (Refereed)
Abstract [en]

An inference method for Gaussian process augmented state-space models are presented. This class of grey-box models enables domain knowledge to be incorporated in the inference process to guarantee a minimum of performance, still they are flexible enough to permit learning of partially unknown model dynamics and inputs. To facilitate online (recursive) inference of the model a sparse approximation of the Gaussian process based upon inducing points is presented. To illustrate the application of the model and the inference method, an example where it is used to track the position and learn the behavior of a set of cars passing through an intersection, is presented. Compared to the case when only the state-space model is used, the use of the augmented state-space model gives both a reduced estimation error and bias.

Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers (IEEE), 2020
Keywords
Gaussian Process, Learning, Online Learning, Sensor fusion, Extended Kalman Filter, WASP_publications
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-167484 (URN)10.23919/FUSION45008.2020.9190245 (DOI)000659928700072 ()978-0-578-64709-8 (ISBN)978-1-7281-6830-2 (ISBN)
Conference
2020 23rd International Conference on Information Fusion (FUSION 2020), Virtual, Pretoria, South Africa, July 6-9, 2020.
Projects
WASP
Funder
Wallenberg AI, Autonomous Systems and Software Program (WASP)
Note

Funding agencies:This work was partially supported by the Wallenberg AI, Autonomous Systems and Software Program (WASP) funded by the Knut and Alice Wallenberg Foundation.

Available from: 2020-07-09 Created: 2020-07-09 Last updated: 2024-05-13
2. Online Joint State Inference and Learning of Partially Unknown State-Space Models
Open this publication in new window or tab >>Online Joint State Inference and Learning of Partially Unknown State-Space Models
2021 (English)In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 69, p. 4149-4161Article in journal (Refereed) Published
Abstract [en]

A computationally efficient method for online joint state inference and dynamical model learning is presented. The dynamical model combines an a priori known, physically derived, state-space model with a radial basis function expansion representing unknown system dynamics and inherits properties from both physical and data-driven modeling. The method uses an extended Kalman filter approach to jointly estimate the state of the system and learn the unknown system dynamics, via the parameters of the basis function expansion. The key contribution is a computational complexity reduction compared to a similar approach with globally supported basis functions. By using compactly supported radial basis functions and an approximate Kalman gain, the computational complexity is considerably reduced and is essentially determined by the support of the basis functions. The approximation works well when the system dynamics exhibit limited correlation between points well separated in the state-space domain. The method is exemplified via two intelligent vehicle applications where it is shown to: (i) have competitive system dynamics estimation performance compared to the globally supported basis function method, and (ii) be real-time applicable to problems with a large-scale state-space.

Place, publisher, year, edition, pages
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 2021
Keywords
Computational modeling, Computational complexity, State-space methods, Kalman filters, Vehicle dynamics, System dynamics, System identification; WASP_publications
National Category
Control Engineering Signal Processing
Identifiers
urn:nbn:se:liu:diva-178181 (URN)10.1109/TSP.2021.3095709 (DOI)000682123900009 ()
Funder
Wallenberg AI, Autonomous Systems and Software Program (WASP)
Note

Funding: Wallenberg AI, Autonomous Systems and Software Program (WASP) - Knut and Alice Wallenberg Foundation

Available from: 2021-08-11 Created: 2021-08-11 Last updated: 2024-05-13
3. On the Relationship Between Iterated Statistical Linearization and Quasi–Newton Methods
Open this publication in new window or tab >>On the Relationship Between Iterated Statistical Linearization and Quasi–Newton Methods
2023 (English)In: IEEE Signal Processing Letters, ISSN 1070-9908, E-ISSN 1558-2361, Vol. 30, p. 1777-1781Article in journal (Refereed) Published
Abstract [en]

This letter investigates relationships between iterated filtering algorithms based on statistical linearization, such as the iterated unscented Kalman filter (IUKF), and filtering algorithms based on quasi–Newton (QN) methods, such as the QN iterated extended Kalman filter (QN–IEKF). Firstly, it is shown that the IUKF and the iterated posterior linearization filter (IPLF) can be viewed as QN algorithms, by finding a Hessian correction in the QN –IEKF such that the IPLF iterate updates are identical to that of the QN–IEKF. Secondly, it is shown that the IPLF/ IUKF update can be rewritten such that it is approximately identical to the QN–IEKF, albeit for an additional correction term. This enables a richer understanding of the properties of iterated filtering algorithms based on statistical linearization.

Place, publisher, year, edition, pages
IEEE, 2023
Keywords
Nonlinear filtering, statistical linearization, quasi-newton
National Category
Control Engineering Probability Theory and Statistics
Identifiers
urn:nbn:se:liu:diva-199896 (URN)10.1109/lsp.2023.3336559 (DOI)001118683900002 ()2-s2.0-85178002018 (Scopus ID)
Projects
Wallenberg AI, Autonomous Systems and Software Program (WASP)
Funder
Knut and Alice Wallenberg Foundation, 304093
Note

Funding: Wallenberg AI, Autonomous Systems and Software Program

Available from: 2024-01-03 Created: 2024-01-03 Last updated: 2024-05-13

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