Linear minimum mean square error estimation for discrete-time Markovian jump linear systems

• Published in: IEEE transactions on automatic control Vol. 39; no. 8; pp. 1685 - 1689
• Main Author: Costa, O.L.V.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.08.1994; Institute of Electrical and Electronics Engineers
• Subjects: Applied sciences; Brazil Council; Computer science; control theory; systems; Control theory. Systems; Equations; Estimation error; Exact sciences and technology; Linear systems; Mean square error methods; Modelling and identification; Noise reduction; Nonlinear filters; State estimation; Uncertainty; Vectors; Markov chain; Linear system; Least squares method; Jump process; Discrete system; Linear estimation; State estimation; Recursive filtering
• ISSN: 0018-9286
• DOI: 10.1109/9.310052

The linear minimum mean square error estimator (LMMSE) for discrete-time linear systems subject to abrupt changes in the parameters modeled by a Markov chain /spl theta/(k)/spl epsiv/{1...,N} is considered. The filter equations are derived from geometric arguments in a recursive form, resulting in an on-line algorithm suitable for computer implementation. The author's approach is based on estimating x(k)1/sub {/spl theta/(k/=i}) instead of estimating directly x(k). The uncertainty introduced by the Markovian jumps increases the dimension of the filter to N(n+1), where n is the dimension of the state variable. An example where the dimension of the filter can be reduced to n is presented, as well as a numerical comparison with the IMM filter.< >