Linear estimation of the frequency and phase of a noisy sinusoid

Abstract

We extend the study in [1] 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 [3] 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 [I]. The second is based on the approach in [4] but incorporates our improved observation model. © 2008 IEEE.