Improved estimation of the frequency of a single sinusoid in noise using a new measurement model

The problem of estimating the frequency of a single sinusoid in white Gaussian noise is addressed. Results in the literature are based on a model for the observed signal phase that was first proposed in Tretter (1985). A new model for the observed signal phase is proposed here that models the observed phase noise more accurately, especially for low signal-to-noise ratios (SNR). Two estimators are designed using these two measurement models, namely, the Kalman filter and the maximum likelihood estimator. Their mean square estimation error performances are then compared using simulations, and it is shown that the estimators based on the new measurement model perform better at low SNR. The Kalman filter makes use of prior statistical knowledge of the signal and noise models, and thus is able to achieve a lower threshold SNR. In particular, the Kalman filter based on the new measurement model has the lowest threshold SNR.