Investigation of the universal optimal method of finite-time and spectral-finite processing of navigation signals of aircraft instruments in conditions of complete and incomplete a priori certainty


Аuthors

Fedorinov A. Y.*, Ivanov Y. P.

Saint Petersburg State University of Aerospace Instrumentation, 67, Bolshaya Morskaya str., Saint Petersburg, 190000, Russia

*e-mail: fedorinov_asperant_accaunt@mail.ru

Abstract

In the theory of measuring information processing, new approaches have been developed to finite-time and spectral-finite methods of signal processing (filtering). The signal filtering procedure is the most important task in the field of information processing. The article will explore the key features of these algorithms. These approaches are based on the orthogonal projection theorem and are optimal by the criterion of the minimum amount of error variance. The approaches are capable of producing linear recurrent estimates of non-Markov signals with correlated and uncorrelated interference. At the moment, the engineering community is making extensive use of Kalman filtering. The proposed algorithms will have an advantage over the Kalman filter. The estimation algorithms obtained on the basis of this approach coincide in accuracy with Kalman filtering and are applicable to a wide class of signal and interference models. In this paper, recurrent sums of error variances of current and interpolated estimates, optimal by the criterion of minimum, linear algorithms for filtering signals under conditions of various a priori certainty against the background of correlated and white noise, with memory provision for the measurements obtained from the beginning of work, will be investigated. The optimal estimation algorithms obtained on the basis of the properties of the orthogonal projection theorem are universal for a wide class of signal and interference models, independent of the presence of the markovity property of the signal and the correlation of measurement interference, coinciding in accuracy with Kalman filtering, simpler in their implementation, due to the adaptability property, they have increased noise immunity and robustness, at the same time With optimal filtering, optimal signal interpolation is provided The simulation was carried out in the Mathcad environment. Currently, the following algorithms have been implemented and studied: finite-time and spectral-finite; with/without feedback; adaptive / non-adaptive; with or without known interference, and their combinations.

Keywords:

finite-time processing, spectral-finite estimation of navigation signals, optimality, versatility of application, adaptive filtering, orthogonal projection theorem, Duba theorem

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