Stationary filter for linear minimum mean square error estimator of discrete-time Markovian jump systems

We derive in this paper a stationary filter for the linear minimum mean square error estimator (LMMSE) of discrete-time Markovian jump linear systems (MJLSs). We obtain the convergence of the error covariance matrix of the LMMSE to a stationary value under the assumption of mean square stability of the MJLS and ergodicity of the associated Markov chain. It is shown that there exists a unique solution for the stationary Riccati filter equation and, moreover, this solution is the limit of the error covariance matrix of the LMMSE. The advantage of this scheme is that it is very easy to implement and all calculations can be performed off-line, leading to a linear time-invariant filter.

[1]  C. Desoer,et al.  Linear System Theory , 1963 .

[2]  Nasser E. Nahi,et al.  Optimal recursive estimation with uncertain observation , 1969, IEEE Trans. Inf. Theory.

[3]  M. Athans,et al.  State Estimation for Discrete Systems with Switching Parameters , 1978, IEEE Transactions on Aerospace and Electronic Systems.

[4]  Mohamed T. Hadidi,et al.  Linear recursive state estimators under uncertain observations , 1978 .

[5]  Jitendra K. Tugnait,et al.  Detection and estimation for abruptly changing systems , 1981, 1981 20th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[6]  Jitendra Tugnait,et al.  Adaptive estimation and identification for discrete systems with Markov jump parameters , 1981, 1981 20th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[7]  Y. Bar-Shalom,et al.  The interacting multiple model algorithm for systems with Markovian switching coefficients , 1988 .

[8]  M. Fragoso,et al.  Stability Results for Discrete-Time Linear Systems with Markovian Jumping Parameters , 1993 .

[9]  O. Costa.  Linear minimum mean square error estimation for discrete-time Markovian jump linear systems , 1994, IEEE Trans. Autom. Control..

[10]  R. Elliott,et al.  Adaptive control of linear systems with Markov perturbations , 1998, IEEE Trans. Autom. Control..

[11]  Qing Zhang.  Optimal Filtering of Discrete-Time Hybrid Systems , 1999 .

[12]  Qing Zhang,et al.  Hybrid filtering for linear systems with non-Gaussian disturbances , 2000, IEEE Trans. Autom. Control..

[13]  Michael O. Kolawole,et al.  Estimation and tracking , 2002 .