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

In this note, a minimum entropy filtering algorithm is presented for a class of multivariate dynamic stochastic systems, which are represented by a set of time-varying difference equations and are subjected to the multivariate non-Gaussian stochastic inputs. Several new concepts including the hybrid random vector, hybrid probability and hybrid entropy are firstly established to describe the probabilistic property of the estimation errors. New relationships are provided 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 sub-optimal filter so that the hybrid entropy of the estimation error can be minimized. Finally, an improved algorithm is provided through the on-line tuning of the weighting matrices so as to guarantee the local stability of the error system.