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Probability of search object detecting by detection device in their mutual motion in arbitrary paths with changing velocities

Keywords:

V.M. Artyushenko – Dr. Sc. (Eng.), Professor, Head of Department of Information Technology and Management Systems, Technological University (Korolyov, Moscow region) E-mail: artuschenko@mail.ru V.I. Volovach – Dr. Sc. (Eng.), Associate Professor, Head of Department of Information and Electronic Service, Volga Region State University of Service (Togliatti) E-mail: volovach.vi@mail.ru


The article determines the probability of detecting objects of search (unmanned aerial vehicles are taken as an example) by surveillance devices for the case when an object of search and a surveillance device move simultaneously. In this case the motion is regarded as movement along arbitrary paths with changing velocities. We obtained the expression describing nonuniform distribution of probable locations of an object of search for the case when directions of an object are equally probable in the range from 0 to 360°, and its velocity is accurately known and does not change during the process of search. The kinematics of search for mutual motion of an object of search and a surveillance device (detection device) is studied. The case, when direction of object motion is uniformly distributed in a certain sector, is considered. In this case the velocity of the object is not a constant, but a random value, obeying a certain law of distribution. The general case, where an object of search and a detection device moves in complex paths with changing velocities, is considered and analyzed. We obtained the expressions for determining the probability of detecting a search object in discrete and continuous observation of an area in the assumption that search is a random process of Markov type. The properties of the detection flow are determined. It is shown that in the case of continuous observation it is necessary to determine the flow rate of detections, whereas in the case of discrete observation it is necessary to determine elementary probability of detection. We got the expressions for determining the above-mentioned probabilities of detection under the assumption that the values of the elementary probabilities of detection change with time.
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