In this paper it is considered the solution of optimal filtering problem for stochastic differential systems. The spectral method is used for the approximate finding of conditional probability density for the system state. This method is based on representation of the solution for robust Duncan–Mortensen–Zakai equation as the orthogonal series. This approach simplifies the process of solving the problem, making it convenient for the use of computers.
conditional density, Duncan–Mortensen–Zakai equation, optimal filtering problem, spectral method, stochastic system