Iterative algorithms for state estimation of jump Markov linear systems

Author

Doucet, Arnaud ; Andrieu, Christophe

Author_Institution

Dept. of Eng., Cambridge Univ., UK

Volume

49

Issue

6

fYear

2001

fDate

6/1/2001 12:00:00 AM

Firstpage

1216

Lastpage

1227

Abstract

Jump Markov linear systems (JMLSs) are linear systems whose parameters evolve with time according to a finite state Markov chain. Given a set of observations, our aim is to estimate the states of the finite state Markov chain and the continuous (in space) states of the linear system. In this paper, we present original deterministic and stochastic iterative algorithms for optimal state estimation of JMLSs. The first stochastic algorithm yields minimum mean square error (MMSE) estimates of the finite state space Markov chain and of the continuous state of the JMLS. A deterministic and a stochastic algorithm are given to obtain the marginal maximum a posteriori (MMAP) sequence estimate of the finite state Markov chain. Finally, a deterministic and a stochastic algorithm are derived to obtain the MMAP sequence estimate of the continuous state of the JMLS. Computer simulations are carried out to evaluate the performance of the proposed algorithms. The problem of deconvolution of Bernoulli-Gaussian (BG) processes and the problem of tracking a maneuvering target are addressed

Keywords

Gaussian processes; Markov processes; deconvolution; iterative methods; least mean squares methods; linear systems; sequential estimation; state estimation; stochastic processes; target tracking; Bernoulli-Gaussian processes; JMLS; MMAP sequence estimate; MMSE estimates; computer simulations; continuous state; deconvolution; deterministic iterative algorithms; finite state Markov chain; finite state space Markov chain; iterative algorithms; jump Markov linear systems; maneuvering target tracking; marginal maximum a posteriori sequence estimate; minimum mean square error estimates; optimal state estimation; performance evaluation; stochastic iterative algorithms; Computer simulation; Deconvolution; Iterative algorithms; Linear systems; Mean square error methods; State estimation; State-space methods; Stochastic processes; Target tracking; Yield estimation;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.923304

Filename

923304