Recognition of a Quasiperiodic Sequence Containing Identical Subsequences-Fragments

摘要

The solution to the problem of recognition of a quasiperiodic sequence containing subsequences-fragments is presented. The case is analyzed where (1) the quasiperiodic sequence contains only identical sub-sequences-fragments; (2) the serial numbers of the first terms (the initial times) of the subsequences-fragments are deterministic (not random) but unknown values; (3) the number of subsequences-fragments in the quasiperiodic sequence is unknown; (4) the quasiperiodic sequence is distorted by an uncorrelated additive Gaussian noise with known variance; and (5) the boundaries of the interval of observation of the distorted sequence do not break the first and last subsequences-fragments of the unobservable nondistorted quasiperiodic sequence into two parts. It is established that this problem is a specific problem of testing hypotheses of the mean of a random Gaussian vector. The efficient a posteriori computational algorithm for solving the problem is substantiated. The recursive formulas of stepwise discrete optimization for making decisions according to the maximum likelihood criterion are obtained. The time and space complexities of the algorithm determined by the parameters of the problem are estimated. The results of numerical simulation are presented.