DOI: 10.14489/vkit.2019.01.pp.012-021

Бухалев В. А., Болдинов В. А., Прядкин С. П., Скрынников А. А.
КОМПЛЕКСИРОВАНИЕ ИЗМЕРИТЕЛЯ, ИНДИКАТОРА СИГНАЛА И ПОМЕХИ В НЕЛИНЕЙНОЙ СИСТЕМЕ СО СЛУЧАЙНОЙ СТРУКТУРОЙ
(с. 12-21)

Аннотация. Рассмотрена задача оптимального комплексирования информации, поступающей от измерителя выходного сигнала нелинейной стохастической системы и индикатора случайно изменяющихся помеховых ситуаций. Получен байесовский рекуррентный алгоритм, основанный на теории систем со случайной скачкообразной структурой, марковской математической модели и двухмоментной параметрической аппроксимации законов распределения случайного процесса бета-распределениями. Алгоритм осуществляет взаимосвязанное и одновременное распознавание помеховых ситуаций, а также оценивание величины полезного сигнала.

Ключевые слова:  система со случайной скачкообразной структурой; марковская цепь; двухмоментная параметрическая аппроксимация; байесовский алгоритм; бета-распределение.

Bukhalev V. A., Boldinov V. A., Pryadkin S. P., Scrynnikov A. A.
COMPLEXING OF THE MEASURER, INDICATOR OF SIGNAL AND HINDRANCE IN A NONLINEAR SYSTEM WITH RANDOM STRUCTURE
(pp. 12-21)

Abstract. The article is devoted to the problem of constructing optimal algorithms of complex information processing. Nonlinear stochastic system and the indicator of situations of randomly changing disturbances are considered. The algorithm is based on the methods of Markov theory to the estimation of random processes. Unlike most algorithms based only on signal filtering, mentioned algorithm is focused on the more difficult task: detection, recognition and estimation of true signal-to-noise ratio. Feature of traditional methods of solving such tasks are chronologically sequential scheme of building “detection – recognition – estimation”. Theoretical approach, providing a more accurate, albeit more complex implementation of the solution, is the simultaneous and interrelated recognition and assessment. This approach is used in the methods of synthesis algorithms of information processing, based on the systems theory with Random Jumping Structure (RJS). Despite similarities between the true and false signals generated by modern means of information countermeasures, there are distinctive characteristics that can’t be simulated easily. This characteristic is, for example, the probability distribution of signals. Another characteristic feature is situations of randomly changing disturbances, due to two main reasons: the need to perform electromagnetic compatibility of signals during operation of measurement and information systems and the emergence of a system of random abrupt transients, reducing the effectiveness of its work. This article examines three possible typical situations of the disturbances, when the output signal of the measuring element contains only noise (false signal), only useful (true) signal, half the sum of true and false signals. A nonlinear model for the formation of a useful signal allows one to take into account the actual signal limitations present in control system devices. The goal is to build approximately-optimal algorithm of information processing based on the following concepts: systems theory with RJS, Markov mathematical models, Bayesian approach, two-moment parametric approximation with the help of beta distribution. Received approximately-optimal detection algorithm of the situations of disturbances and estimation of the magnitude of the true signal is described by a closed system of ordinary recurrence equations. Inputs of the algorithm are the measured signal and structure indicator reading, output signals are the probability of the situations of disturbances (structure), estimation of the structure state, estimation of the true signal and its variance. The approach demonstrated in the article proved its effectiveness, as it leads to an acceptable compromise between two conflicting requirements – accuracy of the solution and ease of implementation.

Keywords: Systems theory with random jumping structure; Markov chain; Two-moment parametrical approximation; Bayesian algorithm; Beta distributions.