Algorithms for Optimal Localization of Point-Impulse Sources with a Piecewise-Constant Probability Density Distribution

One of the problems associated with the construction of the optimal strategy for searching for point signal sources that reveal themselves by generating ultrashort impulses at random moments in time is formulated and solved. An exact analytical solution of the problem is obtained for the case when the a priori probability distribution density of the source being sought is specified by a multistage piecewise-constant function. An explicit form of the functional is established that describes the mathematical expectation of the time required to localize a source with the predetermined accuracy. As a result of solving the variational problem, a constructive algorithm for calculating the optimal parameters of a multistage search procedure is constructed, thereby minimizing the average search time. This algorithm is fully formalized and is implemented in a specialized software block.