Recursive maximum likelihood identification of jump Markov nonlinear systems

TL;DR

This paper introduces an online Rao-Blackwellized particle filter method for joint state and parameter estimation in jump Markov nonlinear systems, improving efficiency and accuracy in complex models.

Contribution

It develops a novel recursive approach combining RBPF and EM algorithms for real-time identification of unknown parameters in JMNLS.

Findings

Effective in simulations demonstrating accurate state and parameter estimation.

Reduces estimation error variance through analytical marginalization.

Applicable to real-world localization problems with real data.

Abstract

In this contribution, we present an online method for joint state and parameter estimation in jump Markov non-linear systems (JMNLS). State inference is enabled via the use of particle filters which makes the method applicable to a wide range of non-linear models. To exploit the inherent structure of JMNLS, we design a Rao-Blackwellized particle filter (RBPF) where the discrete mode is marginalized out analytically. This results in an efficient implementation of the algorithm and reduces the estimation error variance. The proposed RBPF is then used to compute, recursively in time, smoothed estimates of complete data sufficient statistics. Together with the online expectation maximization algorithm, this enables recursive identification of unknown model parameters. The performance of the method is illustrated in simulations and on a localization problem in wireless networks using real data.