White Noise Theory of Robust Nonlinear Filtering with Correlated State andObservation Noises

摘要

One purpose of the paper is to remove the asymmetry in the existing 'direct'white noise theory by modeling the state process as the solution of a stochastic differential equation with a 'directly modelled' white noise as the input. It is shown that the solution of such a stochastic differential equation is, indeed, a Markov process. With this formulation, it is straightforward to introduce correlation between the state and observation noises. The other purpose of the paper is to obtain robust nonlinear filtering equation for stochastic dynamical systems with correlated state and observation noises.