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A nonlinear filter based on complex Kalman filter is proposed for estimating a sinusoidal signal and its parameters from the observed signal corrupted by white noise. In the proposed filtering algorithm, the forgetting factor, local iteration and the other techniques are employed in order to upgrade the filter performance. Furthermore, the roles of such techniques above mentioned are also analyzed theoretically. From the results, it is derived that the forgetting factor keeps the mean square error used in the filter more than a certain value, and the iteration improves the accuracy of the estimates by reducing the effects of modeling error and observation noise. On the other hand, it is demonstrated by some simulations that the proposed nonlinear filter is effective as a method for estimating a sinusoidal signal and its frequency under the low SN ratio.

A Consideration on a Nonlinear Filter for Estimating a Sinusoidal Signal and Its Parameters in White Noise