An algorithm for implementing an optimal filtering operator with a prediction based on its synthesized mathematical model for an L-Markov process with a quasi-rational spectrum
Abstract
An algorithm for implementing an optimal filtering operator with a prediction based on its synthesized mathematical model for an L-Markov process with a quasi-rational spectrum
Incoming article date: 08.08.2025A mathematical model has been constructed, an algorithm has been developed, and a program has been written in the Python programming language for calculating the numerical values of the optimal filtering operator with a forecast for an L-Markov process with a quasi-rational spectrum. The probabilistic model of the filtering operator formula has been obtained based on the spectral analysis of L-Markov processes using methods for calculating stochastic integrals, the theory of analytical functions of a complex variable, and methods for correlation and regression analysis. Considered an example of L-Markov process, the values of the optimal filtering operator with a forecast for which it was possible to express in the form of a linear combination of the values of the process at some moments of time and the sum of numerical values of cosines and sines at the same moments. The basis for obtaining the numerical values of the filtering operator was the mathematical model of trigonometric regression with 16 harmonics, which best approximates the process under study and has a minimum
Keywords: random process, L-Markov process, prediction filtering, spectral characteristics, filtering operator