Solving the Problem of Forming Stable and Consistent Estimates of a Correlation Matrix of Observations Using the Method of Dynamic Regularization

Abstract

We analyze the consistency of stable estimates of a correlation matrix of observations at their static and dynamic regularization. We prove the advantage of the dynamic regularization method with the optimal parameter in the context of resolving the contradiction “computational stability–consistency” of sample estimates of a correlation matrix of observations. We obtain the algorithm for computation of the optimal parameter of dynamic regularization that do not use predicted data and do not require additional computational costs.

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References

  1. 1.

    W. D. Wirth, Radar Techniques Using Array Antennas, The Institution of Engineering and Technology, London (2013).

    Google Scholar 

  2. 2.

    D. I. Lekhovytskiy, “To the theory of adaptive signal processing in systems with centrally symmetric receive channels,” EURASIP J. Adv. Signal Process, Article number 33 (2016). https://doi.org/https://doi.org/10.1186/s13634-016-0329-z.

  3. 3.

    D. I. Lekhovitskiy, Yu. I. Abramovich, G. A. Zhuga, and D. S. Rachkov, “Band-diagonal regularization of ML estimates of Gaussian interference correlation matrices in algorithms of antenna arrays adaptation,” Prikladnaya Radioelektronika, Vol. 9, No. 1, 107–121 (2010).

    Google Scholar 

  4. 4.

    Yu. I. Abramovich, N. K. Spencer, and B. A. Johnson, “Band-inverse TVAR covariance matrix estimation for adaptive detection,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 46, No. 1, 375–396 (2010). https://doi.org/https://doi.org/10.1109/TAES.2010.5417169.

  5. 5.

    O. P. Cheremisin, “The efficiency of adaptive algorithm with regularization of sample correlation matrix,” Radiotekh. Elektron., Vol. 27, No. 10, 1933–1942 (1982).

    Google Scholar 

  6. 6.

    A. N. Tikhonov, A. V. Goncharsky, V. V. Stepanov, and A. G. Yagola, Numerical Methods for the Solution of Ill-Posed Problems [in Russian], Nauka, Moscow (1990).

    Google Scholar 

  7. 7.

    Yu. E. Voskoboinikov and A. A. Mitsel’, Modern Problems of Applied Mathematics, Part 1, Lecture Course [in Russian], Tomskiy Gos. Un-t Sistem Upravleniya i Radioelektroniki (TUSUR), Tomsk (2015).

    Google Scholar 

  8. 8.

    Yu. S. Osipov, F. P. Vasiliev, and M. M. Potapov, Bases of the Dynamical Regularization Method [in Russian], Izd-vo MGU, Moscow (1999).

    Google Scholar 

  9. 9.

    V. Skachkov, V. Chepkyi, H. Bratchenko, H. Tkachuk, and N. Kazakova, “Development of the method for dynamic regularization of selected estimates in the correlation matrices of observations,” Eastern-European J. of Enterprise Technologies, Vol. 6, No. 4 (90), 11–18 (2017). https://doi.org/https://doi.org/10.15587/1729-4061.2017.119264.

  10. 10.

    V. Skachkov, V. Chepkyi, A. Efimchikov, O. Korkin, and A. Dudush “Dynamic regularization parameter optimization of a sample estimate of the correlation matrix of observations by the criterion “computational stability–consistency,” in: Proc. 2019 IEEE 2nd Ukraine Conference on Electrical and Computer Engineering (UKRCON) (Lviv, Ukraine, 2–6 July, 2019), IEEE (2019), pp. 18–23. DOI: https://doi.org/10.1109/UKRCON.2019.8879946.

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Correspondence to V. V. Skachkov.

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Translated from Kibernetyka ta Systemnyi Analiz, No. 1, January–February, 2021, pp. 94–103.

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Skachkov, V.V., Chepkii, V.V., Yefymchykov, O.M. et al. Solving the Problem of Forming Stable and Consistent Estimates of a Correlation Matrix of Observations Using the Method of Dynamic Regularization. Cybern Syst Anal 57, 82–90 (2021). https://doi.org/10.1007/s10559-021-00331-3

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Keywords

  • regularization
  • consistency
  • stability
  • convergence
  • estimate