Geodesic
Optimal detection of given number of identical subsequences in quasiperiodic sequence
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 2 (1999) no. 4, pp. 333-349 
A. V. Kel'manov; S. A. Khamidullin. Optimal detection of given number of identical subsequences in quasiperiodic sequence. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 2 (1999) no. 4, pp. 333-349. http://geodesic.mathdoc.fr/item/SJVM_1999_2_4_a3/
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     author = {A. V. Kel'manov and S. A. Khamidullin},
     title = {Optimal detection of given number of identical subsequences in quasiperiodic sequence},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {333--349},
     year = {1999},
     volume = {2},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_1999_2_4_a3/}
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The problem of the detection of given number of identical subsequences in quasiperiodic sequence distorted by the uncorrelated Gaussian interference with a known dispersion is studied. The aposteriori computing algorithm for the solution to this problem is justified. The case is considered, when the boundaries of an interval of the beginning and ending of the observations above the distorted sequence do not break the first and the last subsequence of hidden quasiperiodic sequence into two parts, and the instants of the begining of the subsequences are the determined values. It is established that the given problem is a particular problem of the test of the hypothesis about the mean of the Gaussian random vector. The recursion formulas of step by step discrete optimization ensuring maximum likelihood decsion are obtained. The estimation of temporary and capacitive of the algorithm is given. The outcomes of the numerical modeling are adduced.

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