On Sequential Learning for Parameter Estimation in Particle Algorithms for State-Space Models

Abstract

Particle methods, also known as Sequential Monte Carlo, have been ubiquitous for Bayesian inference for state-space models, particulary when dealing with nonlinear non-Gaussian scenarios. However, in many practical situations, the state-space model contains unknown model parameters that need to be estimated simultaneously with the state. In this paper, We discuss a sequential analysis for combined parameter and state estimation. An online learning method is proposed to approach the distribution of the model parameter by tuning a flexible proposal mixture distribution to minimize their Kullback-Leibler divergence. We derive the sequential learning method by using a truncated Dirichlet processes normal mixture and present a general algorithm under a framework of the auxiliary particle filtering. The proposed algorithm is verified in a blind deconvolution problem, which is a typical state-space model with unknown model parameters. Furthermore, in a more challenging application that we call meta-modulation, which is a more complex blind deconvolution problem with sophisticated system evolution equations, the proposed method performs satisfactorily and achieves an exciting result for high efficiency communication.