Properties of the IEEE-STD-1057 four-parameter sine wave fit algorithm

The IEEE Standard 1057 (IEEE-STD-1057) provides algorithms for fitting the parameters of a sine wave to noisy discrete time observations. The fit is obtained as an approximate minimizer of the sum of squared errors, i.e. the difference between observations and model output. The contributions of this paper include a comparison of the performance of the four-parameter algorithm in the standard with the Cramér-Rao lower bound on accuracy, and with the performance of a nonlinear least squares approach. It is shown that the algorithm of IEEE-STD-1057 provides accurate estimates for Gaussian and quantization noise. In the Gaussian scenario it provides estimates with performance close to the derived lower bound. In severe conditions with noisy data covering only a fraction of a period, however, it is shown to have inferior performance compared with a one-dimensional search of a concentrated cost function. Keywords—IEEE standards, Measurement standards, Signal analysis, Frequency estimation, Electronic equipment testing