Outlier-robust Kalman Filtering through Generalised Bayes

TL;DR

This paper introduces a new robust Bayesian filtering method that effectively handles outliers in state-space models, combining theoretical robustness with computational efficiency for nonlinear systems.

Contribution

It presents a novel closed-form Bayesian update rule that is robust to outliers and integrates with existing filtering methods like the extended and ensemble Kalman filter.

Findings

Outperforms existing robust filtering methods in accuracy.

Maintains computational efficiency for nonlinear models.

Effective in diverse applications like object tracking and neural network learning.

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.