On SNR estimation using IEEE-STD-1057 three-parameter sine wave fit

In this paper, theoretical properties of a maximum-likelihood (ML) estimator of signal-to-noise ratio (SNR) is discussed. The three-parameter sine fit algorithm is employed on a finite and coherently sampled measurement set corrupted by additive white Gaussian noise. Under the Gaussian noise model, the least squares solution provided by the three-parameter sine fit is also ML estimator. Exact distribution and finite sample properties of the SNR estimate are derived. Moreover, an explicit expression for the mean squared error (MSE) of the estimator is given. Simulation results are shown to verify the underlying theoretical results.