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Noise Robust Online Inference for Linear Dynamic Systems

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  • Saikat Saha

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.

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  • Saikat Saha, 2015. "Noise Robust Online Inference for Linear Dynamic Systems," Papers 1504.05723, arXiv.org.
  • Handle: RePEc:arx:papers:1504.05723
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    1. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," Review of Economic Studies, Oxford University Press, vol. 65(3), pages 361-393.
    2. Nicolas Chopin, 2002. "Central Limit Theorem for Sequential Monte Carlo Methods and its Applications to Bayesian Inference," Working Papers 2002-44, Center for Research in Economics and Statistics.
    3. Marco J. Lombardi & Simon J. Godsill, 2004. "On-line Bayesian estimation of AR signals in symmetric alpha-stable noise," Econometrics Working Papers Archive wp2004_05, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
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