Localization of Point Sources with Random Spatial Position and Random Discipline of Pulse Generation Alexander L. Reznik (1) , Alexander V. Tuzikov (2) , Andrey V. Torgov (1) , Aleksander A. Soloviev (1) , Vasiliy A. Kovalev (2) (1) Institute of Automation and Electrometry SB RAS, Novosibirsk (2) United Institute of Informatics Problems, National Academy of Sciences, Minsk Abstract. The methods and speed-optimal algorithms oriented to spatial localization of pulsed-point sources manifesting themselves at random time by generation of instantaneous delta pulses are discussed. Optimal search procedures have been proposed that are focused on the localization of random pulsed-point objects in standard and advanced search modes (for example, in the absence of a priori information about the intensity of the source or when its density is unknown within the search interval). Keywords: optimal search, random pulsed-point source, localization accuracy, receiver. 1 Introduction Research on the optimal search for random pulse-point objects is subject of current interest for many scientific and technical disciplines. The need to conduct them arises in the design of various electron-optical converters and detectors [1]; in the tasks of the suppression of impulse noise on noisy and low-contrast images [2]; in the development of methods for tech troubleshooting, appearing in a form of the alternating equipment failures [3]; in problems of detecting radioactive sources using systems consisting of one or several sensors [4], in radio physics and radio astronomy, when searching for sources of gravitational waves [5] and in many other applications. This paper presents the methods and algorithms for the speed-optimal search for point Poisson sources that manifest themselves at random time by generation of instantaneous delta pulses. The optimal search algorithm should, as a rule, satisfy one of two requirements: minimize the total search effort required to detect an object; or maximize the total probability of detection in the presence of limited search effort. The point-pulsed source will be understood below as an object of negligibly small angular dimensions (mathematical point), having a random distribution on the abscissa axis with a priori probability density f(x) and radiating infinitely short pulses (-functions) with Poisson intensity λ. Thus, the time intervals between pulses are a random variable t with an exponential probability density h(t) = λexp(-λt). The search for an object is carried out with the help of a recording device having a tunable «window» with an arbitrarily time function. The pulse is fixed if the active object that initiated the pulse is in the «view window» of the recording device. Otherwise, the pulse is considered to be missed. When registering the pulse, the window narrows, and (as a result) the position of the source is determined more accurately. It is required for the minimum (in statistical terms) time to find a source with an accuracy of  2 Single-step search algorithms Introducing the binary function x         otherwise, , 0 , device receiving the of window view the in is moment time at the point the if , 1 ) , ( t x t x u describing the view window at time t, we obtain the average time from the start of the search to the registration of the first pulse:              0 0 0 . ) ) , ( exp( ) , ( ) ( t d x u t x u x tf dx dt      Copyright © 2019 for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).