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 theta(k) E {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. Our approach is based on estimating x(k)1{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 [2].