Linear Estimation of the Frequency and Phase of a Noisy Sinusoid

We extend the study in Fu and Kam (2006) of estimating the frequency and carrier phase of a noisy sinusoid. We show that when the improved observation model is used, the linear regression estimator developed in Tretter (1985) is suboptimal. Two generalized least-squares estimators, namely, the weighted least-squares estimator and the linear minimum variance estimator, are then formulated. To avoid phase unwrapping, we propose two new frequency estimators by using the differenced phase. The first is based on the ML estimator derived in (Fu and Kam). The second is based on the approach in Kay (1991) but incorporates our improved observation model.