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

The problem of interacting multiple model (IMM) estimation for jump Markov linear systems with unknown measurement noise covariance is studied. The system state and the unknown covariance are jointly estimated, where the unknown covariance is modelled as a random matrix according to an inverse-Wishart distribution. For the IMM estimation with random matrices, one difficulty encountered is the combination of a set of weighted inverse-Wishart distributions. Instead of using the moment matching approach, this difficulty is overcome by minimising the weighted Kullback-Leibler divergence for inverse-Wishart distributions. It is shown that a closed-form solution can be derived for the optimisation problem and the resulting solution coincides with an inverse-Wishart distribution. Simulation results show that the proposed filter outperforms the previous work using the moment matching approach.