Identification of jump Markov linear models using particle filters

TL;DR

This paper introduces a novel EM-based algorithm leveraging particle filters and MCMC methods to efficiently identify jump Markov linear models, which are challenging due to their hybrid discrete-continuous structure.

Contribution

The paper presents a new EM algorithm that exploits the model's linear Gaussian substructure and combines particle filters with MCMC for improved parameter estimation.

Findings

Efficient maximum likelihood estimation for jump Markov linear models.

Utilizes particle filters with MCMC to handle nonlinear state smoothing.

Exploits conditionally linear Gaussian structure for computational efficiency.

Abstract

Jump Markov linear models consists of a finite number of linear state space models and a discrete variable encoding the jumps (or switches) between the different linear models. Identifying jump Markov linear models makes for a challenging problem lacking an analytical solution. We derive a new expectation maximization (EM) type algorithm that produce maximum likelihood estimates of the model parameters. Our development hinges upon recent progress in combining particle filters with Markov chain Monte Carlo methods in solving the nonlinear state smoothing problem inherent in the EM formulation. Key to our development is that we exploit a conditionally linear Gaussian substructure in the model, allowing for an efficient algorithm.