Enumerative combinatorics
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The detection problem for a group of moving targets is a generalization of the classical detection problem for a single still target. Synthesis methods for joint detection and phase coordinate measurement for objects in the group are being developed in the theory of random streams of events. In this work, we propose a Poisson approximation for a Bernoullian stream of signals generated by a group target and observed in noises for small signal/noise ratios. Using this approximation, we can significantly simplify optimal detection and parameter estimation for a group target which are hard to implement exactly. Developing suboptimal algorithms is an important problem for a number of technical applications, including, in particular, radioand hydrolocation.