Linear minimum mean square error estimation for discrete-time Markovian jump linear systems
- 1 August 1994
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 39 (8) , 1685-1689
- https://doi.org/10.1109/9.310052
Abstract
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.<>Keywords
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