Abstract
This paper describes a new attempt at the non-linear state estimation for the stochastic environmental system with varying S/N ratio. A recursive algorithm of estimating higher order statistical quantities of arbitrary function type, not to mention mean or variance, is obtained by introducing a new expansion form of Bayes' theorem. Furthermore, this method is widely applicable for the actual case when the random fluctuation is of non-Gaussian type. The algorithm proposed in this paper agrees completely with the well-known Kalman filtering theory as a simplified special case when the stochastic system is a linear type with Gaussian random excitation. Finally, the validity and effectiveness of the theory are experimentally confirmed by applying it to the actually observed room acoustic data and the road traffic noise data.
