Scheduled System Maintenance:
Some services will be unavailable Sunday, March 29th through Monday, March 30th. We apologize for the inconvenience.
By Topic

Online Bayesian estimation of transition probabilities for Markovian jump systems

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

2 Author(s)
Jilkov, V.P. ; Dept. of Electr. Eng., Univ. of New Orleans, LA, USA ; Li, X.R.

Markovian jump systems (MJSs) evolve in a jump-wise manner by switching among simpler models, according to a finite Markov chain, whose parameters are commonly assumed known. This paper addresses the problem of state estimation of MJS with unknown transition probability matrix (TPM) of the embedded Markov chain governing the jumps. Under the assumption of a time-invariant but random TPM, an approximate recursion for the TPMs posterior probability density function (PDF) within the Bayesian framework is obtained. Based on this recursion, four algorithms for online minimum mean-square error (MMSE) estimation of the TPM are derived. The first algorithm (for the case of a two-state Markov chain) computes the MMSE estimate exactly, if the likelihood of the TPM is linear in the transition probabilities. Its computational load is, however, increasing with the data length. To limit the computational cost, three alternative algorithms are further developed based on different approximation techniques-truncation of high order moments, quasi-Bayesian approximation, and numerical integration, respectively. The proposed TPM estimation is naturally incorporable into a typical online Bayesian estimation scheme for MJS [e.g., generalized pseudo-Bayesian (GPB) or interacting multiple model (IMM)]. Thus, adaptive versions of MJS state estimators with unknown TPM are provided. Simulation results of TPM-adaptive IMM algorithms for a system with failures and maneuvering target tracking are presented.

Published in:

Signal Processing, IEEE Transactions on  (Volume:52 ,  Issue: 6 )