Résumé
Minimum mean square error estimation for linear systems with Markov jump parameters is addressed. The jump variable is assumed to be observed, however only cluster information is taken into account in the filter design, allowing one to seek for the best implementable estimator via the cardinality and choice of the clusters. With this new approach we introduce a set of filters that can be compared in terms of performance according to the refines of clusters of the Markov chain. Moreover, it includes as particular cases the well known Kalman filter with as many clusters as Markov states, as well as the linear Markovian estimator with only one cluster. The Riccati-like formulas for pre-computation of gains are given, and we explore the trade-off between complexity and performance via numerical examples.