  The problem of analyzing the Ito stochastic differential system and its
filtering has received attention. The classical approach to accomplish
filtering for the Ito SDE is the Kushner equation. In contrast to the classical
filtering approach, this paper presents filtering for the stochastic
differential system affected by weakly coloured noise. As a special case, the
process can be regarded as the Ornstein-Uhlenbeck (OU) process. The theory of
this paper is based on a pioneering contribution of Stratonovich involving the
perturbation-theoretic approach to noisy dynamical systems in combination with
the notion of the filtering density evolution. Making the use of the filtering
density evolution equation, the stochastic evolution of condition moment is
derived. A scalar Duffing system driven by the OU process is employed to test
the effectiveness of the filtering theory of the paper. Numerical simulations
involving four different sets of initial conditions and system parameters are
utilized to examine the efficacy of the filtering algorithm of this paper.
