Развитие теории оптимальных динамических измерений

В работе представлен обзор результатов как аналитического исследования задач оптимального динамического измерения, так и результатов в области разработки алгоритмов численных методов для решения задач теории оптимальных динамических измерений. Основным положением теории оптимальных динамических измерений является моделирование искомого входящего сигнала как решения задачи оптимального управления с минимизацией функционал штрафа, в котором оценивается расхождение выходящих моделируемого и наблюдаемого сигналов. Данная теория появилась как новый подход для восстановления динамически искаженных сигналов. Математическая модель сложного измерительного устройства построена как система леонтьевского типа, начальное состояние которой отражает условие Шоуолтера - Сидорова. Первоначально математическая модель учитывала только инерционность устройства измерения, позже математическая модель стала учитывать возникающие в измерительном устройстве резонансы и деградацию устройства с течением времени. Последние результаты учитывают случайные помехи, и уже здесь сложилось несколько подходов: первый подход основан на производной Нельсона - Гликлиха, второй - на очищении наблюдаемого сигнала по методу Пытьева - Чуличкова, третий - на очищении наблюдаемого сигнала с использованием цифровых фильтров, например, Савицкого - Голея или одномерного фильтра Калмана.

Ключевые слова

математическая модель измерительного устройства; система леонтьевского типа; условия Шоуолтера - Сидорова; производная Нельсона - Гликлиха; Винеровский процесс; оптимальное динамическое измерение; наблюдение; метод Пытьева - Чуличкова.

Литература

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