Synthesis of Quasi-Optimal Algorithms Based on the Indirect Method of Nonlinear Filtering

Nonlinear filtering of Markov processes by indi-rect variables is considered. Quasi-optimal algorithms with increased filtering accuracy in conditions of large fluctuations of filtered processes are synthesized. It is shown that the application of the indirect method of nonlinear filtering is more effective in comparison with the direct method which uses Gaussian approximation, where the observation model is an additive mixture of Gaussian noise and signal. At the same time, the indirect method successfully utilizes a functional approach. Dependencies allowing to estimate the phase error variance in the stationary mode on the phase excitation noise variance, as well as dependencies of the phase error skip prob-ability on the excitation noise variance at different values of the signal-to-noise ratio are obtained. It is shown that the consid-ered synthesis method allows to increase filtering accuracy of indirect algorithms synthesized in the first approximation, and the gain increases with the increase of the signal-to-noise ratio. At the same time, it is shown that in the stationary mode with limited phase stochasticity, the average convergence time of indirect estimates is three to four times shorter than the con-vergence time of direct estimates. It is noted that the indirect algorithm has a lower probability of phase error skip.