A design for a general digital filter for state estimation of an arbitrary stochastic sound system

This article describes a new attempt at the design of a general digital filter for the state estimation of a nonstationary nonlinear stochastic sound system. A recursive algorithm for estimating the higher-order statistics of arbitrary-function type, mean, and variance is obtained by introducing a new expansion form of Bayes' theorem. Further, the state probability density function (PDF) can also be estimated in a unified form of orthogonal or nonorthogonal series expansions by using these estimates. This method is widely applicable for cases where the random-noise fluctuation is non-Gaussian. The estimation algorithm proposed in this article agrees completely with a well-known Kalman filtering theory [J. Basic Eng. 82, 35-45 (1960); Kalman and Buchy, J. Basic Eng. 83, 95-108 (1961)], as a simplified special case when the stochastic system is of linear type with Gaussian random excitation. The validity and effectiveness of the proposed theory were confirmed experimentally by applying it to actually observed room acoustic data and road-traffic noise data.