Time-optimal algorithms for detecting and localizing for a random point-pulse source with a unimodal distribution density
Authors: Резник Александр Львович , Соловьев Александр Анатольевич 
Published: July 2022

Сформулирована задача построения оптимального по времени алгоритма поиска с заданной точностью случайного импульсного источника, имеющего одномодальную ступенчатую плотность распределения на интервале поиска. Локализация сигнального источника, обнаруживающего себя в случайные моменты времени генерацией мгновенных импульсов, осуществляется с помощью детекторного приемника с динамически программируемым размером сканирующей апертуры. При разработке оптимальных поисковых алгоритмов основная трудность вызвана необходимостью нахождения точного решения вариационной задачи, связанной с минимизацией многомерного линейного функционала, описывающего среднее (по ансамблю реализаций) время поиска неизвестного точечно-импульсного источника. Показано, что при одномодальной ступенчатой плотности распределения разыскиваемого источника возможно построение оптимальных физически реализуемых алгоритмов поиска с использованием односвязной апертуры детекторного приемника
The issues of constructing high-speed algorithms for searching of pulsed-point sources are considered. A pulsed-point source is treated as an object of negligible angular dimensions (mathematical point). It is supposed having a random distribution density over the search interval; it randomly generates infinitely short impulses (delta functions) Pauses between impulses have an exponential distribution density. Detection and localization of such sources is carried out by a system that includes a receiver with a programmable and arbitrarily time-tunable view window. When the incoming pulse is detected, the position of the searched source is refined and the receiver’s view window decreases; at the next stage, the search continues inside the window where the impulse was fixed. In majority of scientific and technical applications, minimizing the time of detection and localization of random pulsed-point sources requires solving time-consuming variational problems associated with finding extremals of complex integral functionals in the presence of restrictions. As a result, the exact analytical solution of the problem (if it is principally achievable), as a rule, cannot be physically implemented in the form of a scheme with continuous movement of a simply connected scanning window of the receiver. In this paper, we have shown that in the case when the distribution density of a random point source can be represented as an unimodal step function, it is possible to construct a time-optimal and physically realizable strategy for its localization. Algorithms for the localization of random pulsed-point sources that have a multistage single- modal probability distribution density over the search interval and reveal themselves by generating instantaneous impulses at random times are proposed. The parameters of the optimal algorithm are calculated that minimizes the average (in statistical terms, i.e., according to implementation ensemble) the search time for a random source depending on the a priori density of its distribution, the power of the source, and the required localization accuracy.