Amplitude estimation using IEEE-STD-1057 three-parameter sine wave fit: Statistical distribution, bias and variance

There has been a recent interest on the performance of amplitude estimation employing a coherently sampled sinusoidal model to noisy measurements. In [F. Correa Alegria, Bias of amplitude estimation using three-parameter sine fitting in the presence of additive noise, Measurement 42 (2009) 748–756.], several issues regarding the bias of the amplitude estimate were studied. In this work, the results are generalized to include a description of the distribution of the amplitude estimate, with explicit results on bias and variance as by-products. Simple closed form expressions for bias and variance are derived. It is shown that the amplitude estimate in finite samples obeys a Rician distribution. The biased amplitude estimator is also shown to beat all unbiased estimators in terms of mean square error, in a wide spread of scenarios.