A Robust State Filter Against Unmodeled Process And Measurement Noise

TL;DR

This work tackles robust state estimation when both process and measurement noises are imperfect or exhibit outliers. It extends the Weighted Observation Likelihood Filter (WoLF) by adopting a generalized Bayesian posterior and introducing the Robust Loss-based Filter (RoLF), which adds $\Lambda_t$ and $\Omega_t$ to adapt the propagated covariance and process noise. The approach is demonstrated on a 2D motion problem with GARCH-type process noise and mixture measurements, showing improved robustness against extreme outliers, including a focus on the 5% largest losses. Importantly, RoLF preserves the computational efficiency of standard KF variants and is readily extensible to other Kalman filter frameworks.

Abstract

This paper introduces a novel Kalman filter framework designed to achieve robust state estimation under both process and measurement noise. Inspired by the Weighted Observation Likelihood Filter (WoLF), which provides robustness against measurement outliers, we applied generalized Bayesian approach to build a framework considering both process and measurement noise outliers.