Development of the algorithms of correction of correlation matrices

Authors

  • Telman Abbas Aliev Institute of Control Systems, Azerbaijan National Academy of Sciences 9 B. Vahabzade str., Baku, Azerbaijan Republic, AZ1141, Azerbaijan https://orcid.org/0000-0003-2251-9711
  • Naila Fuad Musayeva Institute of Control Systems, Azerbaijan National Academy of Sciences B. Vahabzade Str. 9. AZ1141, Baku, Azerbaijan Republic, Azerbaijan https://orcid.org/0000-0002-8765-5469
  • Ulkar Eldar Sattarova Institute of Control Systems, Azerbaijan National Academy of Sciences B. Vahabzade Str. 9. AZ1141, Baku, Azerbaijan Republic, Azerbaijan https://orcid.org/0000-0002-0174-1412
  • Narmin Eldar Rzayeva Institute of Control Systems, Azerbaijan National Academy of Sciences B. Vahabzade Str. 9. AZ1141, Baku, Azerbaijan Republic, Azerbaijan https://orcid.org/0000-0003-0397-5412

DOI:

https://doi.org/10.15587/1729-4061.2015.54098

Keywords:

stochastic process, identification, technological parameter, noise, noisy signal, correlation function, correlation matrices, normalized estimates, dynamics models

Abstract

Statistical methods are widely used in solving problems of automatic management of industrial objects, as they enable us to determine the dynamic characteristics during normal operation of objects. The statistical correlation method for determining these dynamic characteristics is based on the solution of an integral equation that includes the correlation functions and of the input and output signals. It allows us to obtain the dynamic characteristics of an object without disturbing its regular operation mode.However, the application of these methods for constructing mathematical models of real-life industrial objects presents the following certain difficulty. Interferences and noises are imposed upon the useful signal, hindering the calculation of the estimates of their static characteristics. The paper presents one possible option of creating alternative methods and technologies for eliminating the error induced by noise during the formation of correlation matrices. The proposed general algorithms allow for reducing these matrices to the similar matrices of useful signals.

Two presented alternative robust technologies enable one to solve these problems both in the absence of a correlation between the useful signal and the noise and in the presence of such. The validity of the result is controlled by duplication the obtained estimates of the elements of matrices by both methods. In many real-life industrial objects the need to apply the procedure of normalization of the estimates take place. This leads to an additional error, which also leads to the disruption of adequacy of the results. In the paper, the general methods and technologies for eliminating that error are proposed.

Author Biographies

Telman Abbas Aliev, Institute of Control Systems, Azerbaijan National Academy of Sciences 9 B. Vahabzade str., Baku, Azerbaijan Republic, AZ1141

Doctor of Engineering, Full Member of the Academy of Sciences

Director of institute

Naila Fuad Musayeva, Institute of Control Systems, Azerbaijan National Academy of Sciences B. Vahabzade Str. 9. AZ1141, Baku, Azerbaijan Republic

Doctor of Engineering, professor

Ulkar Eldar Sattarova, Institute of Control Systems, Azerbaijan National Academy of Sciences B. Vahabzade Str. 9. AZ1141, Baku, Azerbaijan Republic

PhD in Engineering

Narmin Eldar Rzayeva, Institute of Control Systems, Azerbaijan National Academy of Sciences B. Vahabzade Str. 9. AZ1141, Baku, Azerbaijan Republic

Researcher

References

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Published

2015-12-22

How to Cite

Aliev, T. A., Musayeva, N. F., Sattarova, U. E., & Rzayeva, N. E. (2015). Development of the algorithms of correction of correlation matrices. Eastern-European Journal of Enterprise Technologies, 6(4(78), 65–76. https://doi.org/10.15587/1729-4061.2015.54098

Issue

Vol. 6 No. 4(78) (2015): Mathematics and Cybernetics - applied aspects

Section

Mathematics and Cybernetics - applied aspects

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Copyright (c) 2015 Telman Abbas Aliev, Naila Fuad Musayeva, Ulkar Eldar Sattarova, Narmin Eldar Rzayeva

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