Filtering for hybrid systems with Markovian and deterministic switching parameters (*)

Abstract

We consider the filtering problem for mixed time Gaussian models with switching. In the case where the switching parameter is a Markov chain, we give (infinite dimensional) exact filters for the signal and for the switching parameter. In a second case, where the switching parameter is an arbitrary non-random (but unknown) function of time, we describe an EM (Expectation Maximization) algorithm for estimating the switching parameter, and derive finite dimensional exact filters necessary for carrying out our EM algorithm. All filters are derived using change of measure techniques