Symbolic-Numeric Computation of Posterior Mean and Variance for a Class of Discrete-Time Nonlinear Stochastic Systems

摘要

This paper proposes a symbolic-numeric Bayesian filtering method for a certain class of discrete-time nonlinear stochastic systems. The prior distribution and the predictive distribution of the output can be non-Gaussian, while the posterior distribution is approximated by a Gaussian distribution. The mean and variance of the posterior distribution are then regarded as functions of the mean and variance at a previous time step, a known input, and an observed output. A set of linear partial differential equations (PDEs) satisfied by these functions is computed by using algorithms for ideals in rings of differential operators offline, and then the set of linear PDEs is numerically solved online to obtain the mean and variance of the current posterior distribution. A numerical example is provided to show the efficiency of the proposed method.