Parameter Estimation in Switching Markov Systems and Unsupervised Smoothing

Stationary jump Markov linear systems (JMLSs) model linear systems whose parameters evolve with time according to a hidden finite state Markov chain. We propose an algorithm for parameter estimation of a recent class of JMLS s called conditionally Gaussian pairwise Markov switching models (CGPMSMs). Our algorithm, named Double-EM (DEM), is based on the expectation-maximization (EM) principle applied twice sequentially. The first EM is applied to the couple (switches, observations) temporarily assumed to be a pairwise Markov chain. The second one is used to estimate the remaining conditional transitions and conditional noise matrices of the CGPMSM. The efficiency of the proposed algorithm is studied via unsupervised smoothing on simulated data. In particular, smoothing results, produced with CGPMSM in an unsupervised manner using DEM, can be more efficient than the ones obtained with the nearest classic conditionally Gaussian linear state-space model based on true parameters and true switches.