A new algorithm for the identification of sinusoidal signal frequency with constant parameters
https://doi.org/10.17586/2226-1494-2022-22-1-18-24
Abstract
The paper presents a solution for identifying the frequency of a sinusoidal signal with constant parameters. The issue can be relevant for compensation of disturbances, control of dynamic objects, and other tasks. The authors propose a method to improve the quality of the estimation of the sinusoidal signal frequency and to ensure exponential convergence to zero of the estimation errors. At the first stage, the sinusoidal signal is presented as an output signal of a linear generator of finite dimension. The signal parameters (amplitude, phase, and frequency) are unknown. At the second stage, the Jordan form of the matrix and the delay operator are applied to parameterize the sinusoidal signal. After a series of special transformations, the simplest equation is obtained containing product of one frequency-dependent unknown parameter and a known function of time. To find the unknown parameter, the authors used the methods of gradient descent and least squares. A new algorithm for the parametrization of a sinusoidal signal is presented. The solution is based on transforming the signal model to a linear regression equation. The problem is solved using gradient descent and least squares tuning methods based on a linear regression equation obtained by parametrizing a sinusoidal signal. The results involve the analysis of the capabilities of the proposed estimation method using computer modeling in the Matlab environment (Simulink). The results confirmed the convergence of the frequency estimation errors to the true values. The developed method can be effectively applied to a wide class of tasks related to compensating or suppressing disturbances described by sinusoidal or multisinusoidal signals, for example, to control a surface vessel with compensation of sinusoidal disturbances.
About the Authors
Kh. T. Nguyen
ITMO University
Russian Federation
Russian Federation
Khac Tung Nguyen — PhD Student
Saint Petersburg, 197101
S. M. Vlasov
ITMO University
Russian Federation
Russian Federation
Sergey M. Vlasov — PhD, Associate Professor
sc 55355689600
Saint Petersburg, 197101
A. A. Pyrkin
ITMO University
Russian Federation
Russian Federation
Anton A. Pyrkin — D.Sc., Full Professor, Dean
sc 26656070700
Saint Petersburg, 197101
I. V. Popkov
ITMO University
Russian Federation
Russian Federation
Ivan V. Popkov — Student
Saint Petersburg, 197101
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Review
For citations:
Nguyen Kh.T., Vlasov S.M., Pyrkin A.A., Popkov I.V. A new algorithm for the identification of sinusoidal signal frequency with constant parameters. Scientific and Technical Journal of Information Technologies, Mechanics and Optics. 2022;22(1):18-24. (In Russ.) https://doi.org/10.17586/2226-1494-2022-22-1-18-24
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