A Gaussian Mixture Smoother for Markovian Jump Linear Systems with non-Gaussian Noises

This paper considers the state smoothing problem for Markovian jump linear systems with non-Gaussian noises which obey Gaussian mixture distributions. On the basis of decomposing the total probability at the point of two adjacent Markov jumping parameters at the current and the next epochs, the posterior probability density of the state for smoothing is derived recursively. Then, through transforming the quotient of two Gaussian mixtures into the corresponding multiplication under the possible two adjacent Markov modes, a recursive Gaussian mixture smoother is designed with the conditional posterior probability density under each hypothesis being approximated by the Gaussian mixture. A maneuvering target tracking example with non-Gaussian noises validates the proposed method.