A new nonlinear filtering algorithm is proposed for the model where the state is a randomly perturbed nonlinear dynamical system and the measurements are made at discrete-time moments in Gaussian noise. It is shown that the approximate scheme based on the algorithm converges to the optimal filter, and the error of the approximation is computed, The algorithm makes it possible to shift offline the most time-consuming operations related to solving the Fokker-Planck equations and computing the integrals with respect to the filtering density.