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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2008, Volume 48, Number 12, Pages 2247–2260
(Mi zvmmf78)
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This article is cited in 5 scientific papers (total in 5 papers)
A posteriori joint detection of a recurring tuple of reference fragments in a quasi-periodic sequence
A. V. Kel'manov, L. V. Mikhailova, S. A. Khamidullin Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, pr. Akademika Koptyuga 4, Novosibirsk, 630090, Russia
Abstract:
The problem of joint detection of a recurring tuple of reference fragments in a noisy numerical quasi-periodic sequence is solved in the framework of the a posteriori (off-line) approach. It is assumed that (i) the total number of fragments in the sequence is known, (ii) the index of the sequence member corresponding to the beginning of a fragment is a deterministic (not random) value, and (iii) a sequence distorted by an additive uncorrelated Gaussian noise is available for observation. It is shown that the problem consists of testing a set of simple hypotheses about the mean of a random Gaussian vector. A specific feature of the problem is that the cardinality of the set grows exponentially as the vector dimension (i.e., the length of the observed sequence) and the number of fragments in the sequence increase. It is established that the search for a maximum-likelihood hypothesis is equivalent to the search for arguments that maximize a special auxiliary objective function with linear inequality constraints. It is shown that this function is maximized by solving the basic extremum problem. It is proved that this problem is solvable in polynomial time. An exact algorithm for its solution is substantiated that underlies an algorithm guaranteeing optimal (maximum-likelihood) detection of a recurring tuple of reference fragments. The results of numerical simulation demonstrate the noise stability of the detection algorithm.
Key words:
numerical quasi-periodic sequence, a posteriori processing, a recurring tuple of reference fragments, optimal noise-proof detection, discrete optimization, efficient algorithm.
Received: 21.04.2007
Citation:
A. V. Kel'manov, L. V. Mikhailova, S. A. Khamidullin, “A posteriori joint detection of a recurring tuple of reference fragments in a quasi-periodic sequence”, Zh. Vychisl. Mat. Mat. Fiz., 48:12 (2008), 2247–2260; Comput. Math. Math. Phys., 48:12 (2008), 2276–2288
Linking options:
https://www.mathnet.ru/eng/zvmmf78 https://www.mathnet.ru/eng/zvmmf/v48/i12/p2247
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