A Posteriori Detection of a Given Number of Truncated Subsequences in a Quasiperiodic Sequence

摘要

The solution to the problem of detecting truncated subsequences in a quasiperiodic sequence is presented. It is assumed that (1) the first (the beginning) and/or last (the ending) members of each subsequence that enters the initial unobservable quasiperiodic sequence are lost (truncated); (2) all nontruncated subsequences that enter the initial quasiperiodic subsequence are identical; (3) the numbers of first members (the instants of beginning) of nontruncated sequences, as well as the numbers of elements corresponding to the truncation boundaries, are determinate (nonrandom), but unknown quantities; (4) the unobservable quasiperiodic sequence that comprises truncated subsequences in disturbed by an additive Gaussian uncorrelated noise whose sequence that comprises truncated subsequences is disturbed by an additive Gaussian uncorrelated noise whose variance is known; (5) the number of subsequences in the quasiperiodic sequence is known. It is found that this problem is a specific problem of testing the hypotheses about the mean of a random Gaussian vector. The efficient a posteriori computational algorithm for the solution of the problem is substantiated. The recurrent formulas for step-by-step discrete optimization are obtained. These formulas allow one to make a decision using the maximum-likelihood criterion. The time and space complexities of the algorithm are evaluated; their dependency on the parameters of the problem is proven. The results of numerical simulation are presented.