Abstract
In the actual random phenomena, the objective signal usually shows a complex fluctuation pattern apart from a standard Gaussian distribution due to the diversified causes of fluctuation. Furthermore, the observation data are very often contaminated by the external noise of arbitrary distribution type. In this paper, a new state estimation algorithm for the stochastic system with a random excitation of non-Gaussian distribution type is proposed by introducing a form of expansion expression with parameter differential type for the conditional probability density function. It is noticeable that the proposed wide sense digital filter is constructed in a hierarchical form based on the direct use of the well-known Kalman's filtering algorithm. Therefore, non-Gaussian properties of the fluctuation and various nonlinear correlation information are reflected hierarchically in this estimation algorithm. Finally, the effectiveness of the theory is experimentally confirmed too by applying it to the actual data in the room acoustical field.
