Outlier-robust Kalman Filtering through Generalised Bayes
This addresses the challenge of robust state estimation in the presence of outliers for applications such as tracking and chaotic systems, representing a strong specific gain rather than a foundational advance.
The paper tackles the problem of online filtering in state-space models with outliers by deriving a novel Bayesian update rule that combines generalised Bayesian inference with filtering methods, resulting in robust performance that matches or outperforms other methods at lower computational cost across applications like object tracking and neural network learning.
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.