On non-linear filtering problems for discrete time stochastic processes

Abstract

In this paper, we shall develop the linear causal analysis for the system consisting of two flows in a real inner product space and give an algorithm for calculating the non-linear filter for a discrete stochastic system which is given by two discrete time stochastic processes, to be called a signal process and an observation process, based upon the theory of ${\mathrm{K}\mathrm{M}}_2\mathrm{O}$-Langevin equations.