Outlier-robust Kalman Filtering through Generalised Bayes

• URL: http://arxiv.org/abs/2405.05646v2
• Date: Tue, 28 May 2024 07:03:49 GMT
• Title: Outlier-robust Kalman Filtering through Generalised Bayes
• Authors: Gerardo Duran-Martin, Matias Altamirano, Alexander Y. Shestopaloff, Leandro Sánchez-Betancourt, Jeremias Knoblauch, Matt Jones, François-Xavier Briol, Kevin Murphy,
• Abstract summary: We derive a novel, provably robust, and closed-form Bayesian update rule for online filtering in state-space models. Our method matches or outperforms other robust filtering methods at a much lower computational cost.
• Score: 45.51425214486509
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We derive a novel, provably robust, 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.

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