Noise Robust Online Inference for Linear Dynamic Systems

We revisit the Bayesian online inference problems for the linear dynamic systems (LDS) under nonGaussian 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.