An online sequential algorithm for the estimation of transition probabilities forjump Markov linear systems

Orguner U., Demirekler M.

AUTOMATICA, vol.42, no.10, pp.1735-1744, 2006 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 42 Issue: 10
  • Publication Date: 2006
  • Doi Number: 10.1016/j.automatica.2006.05.002
  • Journal Name: AUTOMATICA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1735-1744
  • Keywords: jump Markov linear systems, Kullback-Leibler distance measure, transition probability, stochastic approximation, LEIBLER INFORMATION MEASURE, STATE ESTIMATION, ADAPTIVE ESTIMATION, MODELS, IDENTIFICATION, PARAMETERS
  • Middle East Technical University Affiliated: Yes

Abstract

This paper describes a new method to estimate the transition probabilities associated with a jump Markov linear system. The new algorithm uses stochastic approximation type recursions to minimize the Kullback-Leibler divergence between the likelihood function of the transition probabilities and the true likelihood function. Since the calculation of the likelihood function of the transition probabilities is impossible, an incomplete data paradigm, which has been previously applied to a similar problem for hidden Markov models, is used. The algorithm differs from the existing algorithms in that it assumes that the transition probabilities are deterministic quantities whereas the existing approaches consider them to be random variables with prior distributions. (C) 2006 Elsevier Ltd. All rights reserved.