Minimum entropy filtering for multivariate stochastic systems with non-Gaussian noises

In this paper, a minimum entropy filtering algorithm is presented for a class of multivariate dynamic stochastic systems. The concerned systems are represented by a set of time-varying difference equations with multiple non-Gaussian stochastic inputs, and with nonlinearity in the measurement output. Several new concepts including hybrid random vectors, hybrid probability and hybrid entropy are introduced to describe the probabilistic property and randomness of the stochastic estimation errors. New relationships are established between the probability density functions (PDFs) of the multivariate stochastic input and output for different mapping cases. Recursive algorithms are then proposed to design the real-time optimal filters such that hybrid entropy of the estimation error is minimized.