Unbiased estimation of the phase of a sinusoid

Estimation of the phase of a sinusoid is an important problem in signal processing. The usual maximum likelihood estimator is biased and so can produce poor results, especially at low signal-to-noise ratios and/or short data records. It is proven that no unbiased estimator exists; based on the proof, several means of obtaining estimators with less bias than the maximum likelihood estimator are proposed.