519.2.214 Mathematical modeling and comparative analysis of numerical methods for solving the problem of continuousdiscrete filtering of random processes in real time

Valishin A. A. (Bauman Moscow State Technical University), Zaprivoda A. V. (Bauman Moscow State Technical University), Klonov A. S. (Bauman Moscow State Technical University)

STOCHASTIC PROCESS, FILTERING STOCHASTIC PROCESSES, ABSOLUTE OPTIMAL FILTERS, CONDITIONALLY OPTIMAL FILTERS, DISCRETE FILTER OF PUGACHEV, DISCRETE FILTER OF KALMAN, REALTIME PROCESSING


doi: 10.18698/2309-3684-2024-1-93109


With the development of forecasting methods, the exclusion of random effects from the initial information and the studied processes becomes essential. These effects are associated not only with the impossibility of taking into account all factors, but also with the fact that some of them are often not taken into account at all. It is important not to forget about random measurement errors. In the predicted values, due to these effects, a kind of random offset or "noise" is created. Filtering (exclusion) of noise should, of course, increase the reliability and justifiability of forecasts. This article discusses the principles of real-time data filtering. The problem statement is given, as well as the main evaluation criteria that must be met to obtain a satisfactory result. In addition, the principle of operation of the two most common types of filters – absolutely optimal and conditionally optimal - is analyzed, their advantages and disadvantages are described. The application of Kalman and Pugachev filters to a model with two sensors is considered. Some conclusions and recommendations are presented on in which cases it is better to use one or another filter.


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