Maximum Likelihood recursive state estimation using the Expectation Maximization algorithm

A Maximum Likelihood recursive state estimator is derived for non-linear state-space models. The estimator iteratively combines a particle filter to generate the predicted/filtered state densities and the Expectation Maximization algorithm to compute the maximum likelihood filtered state estimate. Algorithms for maximum likelihood state filtering, prediction and smoothing are derived. The conver-gence properties of these algorithms, which are inherited from the Expectation Maximization algorithm and the particle filter, are examined in two examples. For nonlinear state-space systems with linear measurements and additive Gaussian noises, it is shown that the filtering and prediction algorithms reduce to gradient-free optimization in a form of a fixed-point iteration. It is also shown that, with randomized reinitialization, which is feasible because of the simplicity of the algorithm, these methods are able to converge to the Maximum Likelihood Estimate (MLE) of multimodal, truncated and skewed densities, as well as those of disjoint support. (C) 2022 Elsevier Ltd. All rights reserved.

Automated summary

A Maximum Likelihood recursive state estimator is proposed for non-linear state-space models, which combines a particle filter and the Expectation Maximization algorithm. Algorithms for maximum likelihood state filtering, prediction, and smoothing are derived, and their convergence properties are examined, demonstrating the effectiveness of the method in nonlinear systems.