A Posteriori Joint Detection of a Recurring Tuple of Reference Fragments in a Quasi-Periodic Sequence

摘要

The problem of joint detection of a recurring tuple of reference fragments in a noisy numer-ical quasi-periodic sequence is solved in the framework of the a posteriori (off-line) approach. It isassumed that (i) the total number of fragments in the sequence is known, (ii) the index of the sequencemember corresponding to the beginning of a fragment is a deterministic (not random) value, and (iii) asequence distorted by an additive uncorrelated Gaussian noise is available for observation. It is shownthat the problem consists of testing a set of simple hypotheses about the mean of a random Gaussianvector. A specific feature of the problem is that the cardinal ity of the set grows exponentially as the vec-tor dimension (i.e., the length of the observed sequence) and the number of fragments in the sequenceincrease. It is established that the search for a maximum-likelihood hypothesis is equivalent to the searchfor arguments that maximize a special auxiliary objective function with linear inequality constraints. Itis shown that this function is maximized by solving the basic extremum problem. It is proved that thisproblem is solvable in polynomial time. An exact algorithm for its solution is substantiated that underliesan algorithm guaranteeing optimal (maximum-likelihood) detection of a recurring tuple of referencefragments. The results of numerical simulation demonstrate the noise stability of the detection algo-rithm.