Применение методов интервального анализа к цифровой обработке данных корабельного компаса

Abstract

В статье описываются результаты применения методов интервального анализа к цифровой обработке реальной зашумленной информации магнитного курса от корабельного цифрового магнитного компаса. Функционирование алгоритмов оценивалось как при постоянном курсе корабля, так и при выполнении им разворота. Показано, что в условиях неопределенности вероятностных характеристик шумовой компоненты в измерении сигнала, интервальный подход обеспечивает существенно лучшую точность обработки по сравнению со стандартным статистическим подходом.

The paper presents results of application of interval analysis methods to digital processing of noised data from the ship digital magnetic compass. Noises and chaotic corruptions of the data are stipulated by influence of the ship electric mechanisms and power nets. The problem of processing the noised data is formulated as follows: to filtrate off the noised components and to obtain enhanced estimations of the current magnetic course and its accuracy. Data for processing is presented as a short sample of measurements of the magnetic course and any probability characteristics of the summary noise components are unknown. Actually, only reasonable interval constraints on maximal modulus (bounds) onto these components can be shown. Under such uncertainty conditions, the standard mathematical statistics methods can be applied only in a formal way. As the alternative, methods of Interval Analysis can by used, since they do not need information on the probability characteristics of the noising components. In contrast to the statistical approaches, the interval procedures give the guaranteed information set of the process admissible parameters and the guaranteed interval of values of the current magnetic course. For the user the following information is provided. The central point of such interval is given out as a pointwise estimate of the current course, the half of the interval presents the accuracy of this estimate, and the tube of admissible values of the process under observation is also calculated. Investigations of the elaborated interval algorithms were performed both under the constant course of the ship and under performing the turn maneuver. The real primary data of the ship digital magnetic compass were used. For comparison, estimations were calculated on the basis of formal application of the standard least squares method. It was shown that under mentioned uncertainty conditions the interval approach gives crucially better estimates.