A posteriori detecting a quasiperiodic fragment in a numerical sequence

  • Authors:

  • E. Kh. Gimadi;A. V. Kel'Manov;M. A. Kel'Manova;S. A. Khamidullin

  • Affiliations:

  • Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia 630090;Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia 630090;Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia 630090;Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia 630090

  • Venue:
  • Pattern Recognition and Image Analysis
  • Year:
  • 2008

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Abstract

Combinatorial approach to solving the problem of detection of an unknown quasi-periodic fragment in a noisy numerical sequence is considered. The problem is analyzed under the following conditions: (1) the number of repeats is known; (2) the number of the sequence term corresponding to the starting instant of the fragment is a deterministic (non-random) value; and (3) the observed sequence is corrupted by additive Gaussian uncorrelated noise. It is demonstarted that the problem under consideration consists in testing the set of composite hypotheses on the mean of a random Gaussian vector. It is shown that the search for a maximum likelihood hypothesis can be reduced to the search for a maximum of an auxiliary objective function. It is proved that the problem of maximization of this function is NP-hard in the general case. An approximate polynomial algorithm for solving the problem is proposed. To improve the approximation, an algorithm of local search is proposed. Numerical simulation showed reasonable results from the applied point of view.