Minimal dimensional linear filters for discrete-time Markov processes with finite state space

Author

Masi, G. B Di ; Kitsul, P.I.

Author_Institution

Dipartimento di Matematica Pura e Applicata, Padova Univ., Italy

Volume

41

Issue

10

fYear

1996

fDate

10/1/1996 12:00:00 AM

Firstpage

1545

Lastpage

1549

Abstract

We consider a filtering problem for a discrete-time Markov process with k states observed in white Gaussian noise. It is known that in this situation the best linear estimate is given by a k-dimensional Kalman filter, and in some cases the dimension of such a filter can be reduced. Here, using a backward semimartingale description of the process and results from stochastic realization theory, we provide an algorithm for the construction of the minimal dimensional linear filter

Keywords

Gaussian noise; Kalman filters; Markov processes; discrete time systems; filtering theory; realisation theory; state estimation; state-space methods; white noise; backward semimartingale description; best linear estimate; discrete-time Markov processes; finite state space; k-dimensional Kalman filter; minimal dimensional linear filters; stochastic realization theory; white Gaussian noise; Filtering; Filtration; Gaussian noise; Markov processes; Nonlinear filters; Random processes; State-space methods; Statistics; Stochastic resonance; Stochastic systems;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.539442

Filename

539442