Minimal dimension linear filters for stationary Markov processes with finite state space

1 July 1991

journal article
research article
Published by Taylor & Francis in Stochastics and Stochastic Reports

Vol. 36 (1) , 1-19
https://doi.org/10.1080/17442509108833706

Abstract

We consider a filtering problem for a continuous-time Markov process with k states, observed in white Gaussian noise. It is known that in this situation the best linear state estimator is given by a k-dimensional Kalman filter and that in some cases the dimension of such filter can be reduced. Here, using results from stochastic realization theory, we provide necessary and sufficient conditions for the minimality of the dimension of the Kalman filter

Keywords

This publication has 5 references indexed in Scilit:

Realization Theory for Multivariate Stationary Gaussian Processes
SIAM Journal on Control and Optimization, 1985
Reverse time diffusions
Stochastic Processes and their Applications, 1985
A stochastic realization approach to the smoothing problem
IEEE Transactions on Automatic Control, 1979
Statistics of Random Processes I
Published by Springer Nature ,1977
The inverse problem of stationary covariance generation
Journal of Statistical Physics, 1969