Identification of a time-varying parameter of a noiseless sinusoidal signal

We consider a new algorithm for estimating the time-varying parameter $ \omega (t) $ of a noiseless sinusoidal signal $ \alpha (t)\sin (\omega (t)+\varphi ) $. It is assumed that the unknown parameters $ \alpha (t)$ and $ \omega (t)$ of the sinusoidal signal are functions of time that are solutions of linear time-invariant differential equations with known coefficients but unknown initial conditions. The problem is solved using gradient tuning algorithms based on a linear regression equation obtained by parametrizing the original parameter-nonlinear sinusoidal signal. An example and results of computer simulation illustrate the efficiency of the proposed algorithm and also explain the procedure for its synthesis.