Outlier-robust Kalman Filtering through Generalised Bayes

Gerardo Duran-Martin, Matias Altamirano, Alex Shestopaloff, Leandro Sánchez-Betancourt, Jeremias Knoblauch, Matt Jones, Francois-Xavier Briol, Kevin Patrick Murphy
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:12138-12171, 2024.

Abstract

We derive a novel, provably robust, efficient, and closed-form Bayesian update rule for online filtering in state-space models in the presence of outliers and misspecified measurement models. Our method combines generalised Bayesian inference with filtering methods such as the extended and ensemble Kalman filter. We use the former to show robustness and the latter to ensure computational efficiency in the case of nonlinear models. Our method matches or outperforms other robust filtering methods (such as those based on variational Bayes) at a much lower computational cost. We show this empirically on a range of filtering problems with outlier measurements, such as object tracking, state estimation in high-dimensional chaotic systems, and online learning of neural networks.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-duran-martin24a, title = {Outlier-robust Kalman Filtering through Generalised {B}ayes}, author = {Duran-Martin, Gerardo and Altamirano, Matias and Shestopaloff, Alex and S\'{a}nchez-Betancourt, Leandro and Knoblauch, Jeremias and Jones, Matt and Briol, Francois-Xavier and Murphy, Kevin Patrick}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {12138--12171}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/duran-martin24a/duran-martin24a.pdf}, url = {https://proceedings.mlr.press/v235/duran-martin24a.html}, abstract = {We derive a novel, provably robust, efficient, and closed-form Bayesian update rule for online filtering in state-space models in the presence of outliers and misspecified measurement models. Our method combines generalised Bayesian inference with filtering methods such as the extended and ensemble Kalman filter. We use the former to show robustness and the latter to ensure computational efficiency in the case of nonlinear models. Our method matches or outperforms other robust filtering methods (such as those based on variational Bayes) at a much lower computational cost. We show this empirically on a range of filtering problems with outlier measurements, such as object tracking, state estimation in high-dimensional chaotic systems, and online learning of neural networks.} }
Endnote
%0 Conference Paper %T Outlier-robust Kalman Filtering through Generalised Bayes %A Gerardo Duran-Martin %A Matias Altamirano %A Alex Shestopaloff %A Leandro Sánchez-Betancourt %A Jeremias Knoblauch %A Matt Jones %A Francois-Xavier Briol %A Kevin Patrick Murphy %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-duran-martin24a %I PMLR %P 12138--12171 %U https://proceedings.mlr.press/v235/duran-martin24a.html %V 235 %X We derive a novel, provably robust, efficient, and closed-form Bayesian update rule for online filtering in state-space models in the presence of outliers and misspecified measurement models. Our method combines generalised Bayesian inference with filtering methods such as the extended and ensemble Kalman filter. We use the former to show robustness and the latter to ensure computational efficiency in the case of nonlinear models. Our method matches or outperforms other robust filtering methods (such as those based on variational Bayes) at a much lower computational cost. We show this empirically on a range of filtering problems with outlier measurements, such as object tracking, state estimation in high-dimensional chaotic systems, and online learning of neural networks.
APA
Duran-Martin, G., Altamirano, M., Shestopaloff, A., Sánchez-Betancourt, L., Knoblauch, J., Jones, M., Briol, F. & Murphy, K.P.. (2024). Outlier-robust Kalman Filtering through Generalised Bayes. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:12138-12171 Available from https://proceedings.mlr.press/v235/duran-martin24a.html.

Related Material