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 θ(k)ε{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_{θ(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