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

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.<
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