Estimation of an Initial Phase over Extremely Short Record-Length of a Sinewave Signal

It is known that the traditionally used statistically optimal estimator for the initial phase of a sinewave signal possesses a certain systematic bias whose value depends on an unknown initial phase. Due to the inaccuracies involved in estimating an initial phase, such an estimator fails in practice when the record length of a sinusoidal signal is less than one period. This paper presents a new algorithm for unbiased estimation of an initial phase of a sinewave burst in the presence of white noise. Such an algorithm can be thought of as a certain modification of a traditional one that is statistically optimal in the case of infinite record length of a signal under analysis. The proposed algorithm has the same structure and acts as the traditionally used one, but the systematic bias is canceled. The main difference between these two algorithms is that the orthogonal sineweighting functions in the traditional algorithm are substituted by the nonorthogonal functions whose parameters can be established a priori of the measurements. A comparative study of two algorithms is discussed. The proposed method is shown to give a more accurate estimate of an initial phase, rather than the traditional direct form. The analytic results are supplemented by a simulation study.