Noise Robust Online Inference for Linear Dynamic Systems

TL;DR

This paper introduces a noise adaptive Rao-Blackwellized particle filter for linear dynamic systems that robustly handles non-Gaussian noise and spurious observations while being scalable and easy to implement.

Contribution

It proposes a novel RBPF framework using hierarchical Gaussian models to adaptively handle unknown and time-varying non-Gaussian noise in linear systems.

Findings

The proposed RBPF effectively manages non-Gaussian noise in numerical experiments.

The method adapts to changing noise parameters without performance degradation.

Numerical studies demonstrate the filter's robustness and scalability.

Abstract

We revisit the Bayesian online inference problems for the linear dynamic systems (LDS) under non- Gaussian environment. The noises can naturally be non-Gaussian (skewed and/or heavy tailed) or to accommodate spurious observations, noises can be modeled as heavy tailed. However, at the cost of such noise robustness, the performance may degrade when such spurious observations are absent. Therefore, any inference engine should not only be robust to noise outlier, but also be adaptive to potentially unknown and time varying noise parameters; yet it should be scalable and easy to implement. To address them, we envisage here a new noise adaptive Rao-Blackwellized particle filter (RBPF), by leveraging a hierarchically Gaussian model as a proxy for any non-Gaussian (process or measurement) noise density. This leads to a conditionally linear Gaussian model (CLGM), that is tractable. However, this framework requires a valid transition kernel for the intractable state, targeted by the particle filter (PF). This is typically unknown. We outline how such kernel can be constructed provably, at least for certain classes encompassing many commonly occurring non-Gaussian noises, using auxiliary latent variable approach. The efficacy of this RBPF algorithm is demonstrated through numerical studies.