PDF tracking filter design using hybrid characteristic functions

A new tracking filtering algorithm for a class of multivariate dynamic stochastic systems is presented. The system is represented by a set of time-varying discrete systems with non-Gaussian stochastic input and nonlinear output. New concept such as hybrid characteristic functions is introduced to describe the stochastic nature of the dynamic conditional estimation errors, where the key idea is to ensure the distribution of the conditional estimation error to follow a target distribution. For this purpose, the relationships between the hybrid characteristic functions of the multivariate stochastic input and the outputs, and the properties of the hybrid characteristic function are established. A new performance index of the tracking filter is then constructed based on the form of the hybrid characteristic function of the conditional estimation error. An analytical solution, which guarantees the filter gain matrix to be an optimal one, is then obtained.