  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.
