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This paper studies the problem of interacting multiple model (IMM) estimationfor jump Markov linear systems with unknown measurement noise covariance. Thesystem state and the unknown covariance are jointly estimated in the frameworkof Bayesian estimation, where the unknown covariance is modeled as a randommatrix according to an inverse-Wishart distribution. For the IMM estimationwith random matrices, one difficulty encountered is the combination of a set ofweighted inverse-Wishart distributions. Instead of using the moment matchingapproach, this difficulty is overcome by minimizing the weightedKullback-Leibler divergence for inverse-Wishart distributions. It is shown thata closed form solution can be derived for the optimization problem and theresulting solution coincides with an inverse-Wishart distribution. Simulationresults show that the proposed filter performs better than the previous workusing the moment matching approach.

Kullback-Leibler divergence for interacting multiple model estimation with random matrices