A.Y. Fedorinov¹, Yu.P. Ivanov²

¹ˑ² Saint Petersburg State University of Aerospace Instrumentation (Saint Petersburg, Russia)

¹fedorinov.aleksey@mail.ru, ²ypi35@mail.ru

As is known, if the a posteriori distribution density of the estimated signal is not unimodal and symmetric, the optimal estimate according to the criterion of the minimum of the mean square of the error in the class of various statistics should be sought in the class of nonlinear methods for processing measurement results. The best nonlinear estimate in the class of all estimates according to the criterion of the minimum of the mean square of the estimation error in accordance with the Duba theorem is the conditional mathematical expectation of the estimated signal relative to the measurement results. Currently, due to the complexity of obtaining and implementing optimal nonlinear filtering algorithms, many approximate (quasi-optimal) signal estimation methods have been developed. Of the developed methods, the most popular are nonlinear and linear optimal and quasi-optimal Bayesian algorithms for filtering Markov signals. These algorithms are based on finding algorithms in the form of symmetrized stochastic differential and recurrent equations with respect to a posteriori distribution densities for correlated and uncorrelated measurement interference. The analytical solution of these algorithms is very difficult, which leads to the finding of numerous quasi-optimal algorithms based on parametrization of a posteriori distribution densities. Such algorithms are based on the use of decomposition of nonlinear functions of the estimated signal, drift and diffusion coefficients into Taylor series in the vicinity of the estimates obtained, or on Gaussian approximation of distribution laws with the determination of equivalent distribution moments and then the use of generalized Kalman-Busey filter algorithms, and others, providing the required compromise between the accuracy of estimation and the amount of computational costs. The general disadvantage of such algorithms lies in their complexity and in obtaining approximate estimates of the quality of the obtained signal filtering results, and in the lack of universality of the methods under consideration with respect to various models of the estimated signals and measurement interference.

Fedorinov A.Y., Ivanov Yu.P. Method of optimal spectral-finite universal filtering arbitrary signals against arbitrary background interference with a single-mode distribution. Information-measuring and Control Systems. 2025. V. 23. № 6. P. 72−81. DOI: https://doi.org/10.18127/j20700814-202506-05 (in Russian)

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