Recognizing a Quasiperiodic Sequence Composed of a Given Number of Identical Subsequences

摘要

This paper is devoted to the solution of the problem of recognizing a sequence that is composed of a given number of identical subsequences with unknown (determinate) quasiperiodic instants of their beginning under the assumption that this unobservable sequence is corrupted by uncorrelated Gaussian noise whose variance is known; moreover, the first and the last subsequences of the unobservable quasiperiodic sequence are not partitioned by the instants of the commencement and completion of observations of the corrupted sequence. The corresponding computational algorithm is substantiated. It is found that the above problem is a specific problem of testing the hypotheses of the mean value of a Gaussian random vector with a given diagonal covariance matrix. It is shown that the problem can be treated as a combined problem of the simultaneous recognition of the subsequence that has generated the unobservable sequence and detection of the instants of beginning of subsequences in the hidden sequence. The recurrent formulas for the stepwise discrete optimization are obtained. Using these formulas, one can find the maximum value of a likelihood function and make a decision on the basis of the Bayesian and the maximum-likelihood criteria. The time and spece complexities of the algorithm are evaluated. The results of the numerical simulation are presented.