Abstract

Abstract — In this self-contained survey/review paper, we systematically investigate the roots of Bayesian filtering as well as its rich leaves in the literature. Stochastic filtering theory is briefly reviewed with emphasis on nonlinear and non-Gaussian filtering. Following the Bayesian statistics, different Bayesian filtering techniques are developed given different scenarios. Under linear quadratic Gaussian circumstance, the celebrated Kalman filter can be derived within the Bayesian framework. Optimal/suboptimal nonlinear filtering techniques are extensively investigated. In particular, we focus our attention on the Bayesian filtering approach based on sequential Monte Carlo sampling, the so-called particle filters. Many variants of the particle filter as well as their features (strengths and weaknesses) are discussed. Related theoretical and practical issues are addressed in detail. In addition, some other (new) directions on Bayesian filtering are also explored.

Citations

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