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SINUSOIDAL SIGNAL PARAMETERS IDENTIFICATION WITH UNKNOWN VARIABLE AMPLITUDE

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The paper considers the problem of the frequency identification for a biased sinusoidal signal in the absence of measurement noise. It is assumed that the displacement and amplitude of the sinusoidal signal are unknown functions of time. It is accepted that the frequency of the sinusoidal signal is an unknown number, and the displacement and amplitude of the sinusoidal signal can be represented as piecewise linear in the time interval. To estimate the frequency of the sinusoidal signal, an original parametrization procedure was proposed, reducing the original nonlinear equation to the form of a standard linear regression model. After a number of special transformations, the simplest equation was obtained, containing one unknown parameter (the square of the  sinusoidal signal frequency) multiplied by the known time function. To search for this parameter, we used the standard integrated algorithm of identification, which makes it possible to guarantee the robustness of estimates to external disturbances, and also to improve the quality of transients due to the tuning coefficient. The proposed frequency identification algorithm has technical attractiveness and can be used in problems of compensation or suppression of disturbances and/or measurement errors described by harmonic or polyharmonic signals, including for compensation of vertical inertial accelerations in estimating gravity anomalies at a mobile object. To illustrate the efficiency of the proposed identification algorithm, the paper presents the results of computer modeling demonstrating the achievement of the target goals.

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