Technology of calculating robust normalized correlation matrices.

*(English. Russian original)*Zbl 1300.94014
Cybern. Syst. Anal. 47, No. 1, 152-165 (2011); translation from Kibern. Sist. Anal. 2011, No. 1, 164-178 (2011).

Summary: It is shown that, under traditional approach, errors caused by noise disappear after normalizing estimates of noisy signals in diagonal elements of correlation matrices and that, on the contrary, such errors arise in other elements. Hence, the expected result of elimination of errors owing to the transition to normalized correlation matrices is not reached. Algorithms and technologies are proposed for correcting this drawback by obtaining robust normalized correlation matrices analogous to matrices of useful signals. Results of numerous computer experiments are presented that testify to the efficiency of the developed technology.

##### MSC:

94A12 | Signal theory (characterization, reconstruction, filtering, etc.) |

60E99 | Distribution theory |

93E12 | Identification in stochastic control theory |

##### Keywords:

random signal; noise; noisy signal; normalized correlation matrix; robust normalized correlation matrix
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\textit{T. A. Aliev} et al., Cybern. Syst. Anal. 47, No. 1, 152--165 (2011; Zbl 1300.94014); translation from Kibern. Sist. Anal. 2011, No. 1, 164--178 (2011)

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##### References:

[1] | T. A. Aliev, N. F. Musaeva, and U. E. Sattarova, ”Robust technologies for calculating normalized correlation functions,” Cybernetics and Systems Analysis, 46, No. 1, 153–166 (2010). · Zbl 1204.94031 |

[2] | A. N. Tikhonov and V. Ya. Arsenin, Methods of Solving Incorrect Problems [in Russian], Nauka, Moscow (1974). |

[3] | A. A. Samarskii and A. V. Gulin, Numerical Methods [in Russian], Nauka, Moscow (1989). |

[4] | V. V. Solodovnikov, Statistical Dynamics of Linear Systems of Automatic Control [in Russian], Fizmatgiz, Moscow (1960). · Zbl 0095.29703 |

[5] | T. Aliev, Digital Noise Monitoring of Defect Origin, Springer, London (2007). · Zbl 1209.94018 |

[6] | T. Aliev, Robust Technology with Analysis of Interference in Signal Processing, Kluwer/Plenum, New York (2003). · Zbl 1028.93001 |

[7] | T. A. Aliev and Z. A. Amirov, ”Algorithm to choose regularization parameters for statistical identification,” Avtomatika i Telemekhanika, No. 6, 130–139 (1998). · Zbl 1055.93557 |

[8] | T. A. Aliev and N. F. Musaeva, ”Algorithms for determination of dispersion and errors caused by noises of random signals,” Avtometriya, No. 3, 80–92 (1997). |

[9] | T. A. Aliev and N. F. Musaeva, ”An algorithm for eliminating microerrors of noise in the solution of statistical dynamics problems,” Automation and Remote Contr., 59, No. 5, 679–688 (1998). · Zbl 1079.93525 |

[10] | N. F. Musaeva, ”Methodology of calculating robustness as an estimator of statistical characteristics of a noisy signal,” Automatic Contr. and Comput. Sci., 39, No. 5, 53–62 (2005). |

[11] | N. F. Musaeva, ”Robust correlation coefficients as initial data for solving a problem of confluent analysis,” Automatic Contr. and Comput. Sci., 41, No. 2, 76–87 (2007). |

[12] | G. Ya. Mirskii, Hardware Determination of Characteristics of Random Processes [in Russian], Energiya (1967). |

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