An approximate solution of the optimal nonlinear filtering problem for stochastic differential systems by statistical modeling

An algorithm for solving the optimal nonlinear filtering problem by statistical modeling is proposed. It is based on reducing the filtration problem to the analysis of stochastic systems with terminating and branching paths, using a structure similarity of the Duncan–Mortensen–Zakai equations and the generalized Fokker–Planck–Kolmogorov equation. The solution of such problem of analysis can be approximately found by using numerical methods for solving stochastic differential equations and methods for modeling inhomogeneous Poisson flows.