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 o btained as an approximate minimizer of the sum of squared errors, i.e., the difference between observations and model output. The contributions of thi s paper include a comparison of the performance of the tour-parameter algor ithm in the standard with the Cramer-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 qu antization noise. In the Gaussian scenario it provides estimates with perfo rmance close to the derived lower bound. In severe conditions with noisy da ta covering only a fraction of a period, however, it is shown to have infer ior performance compared with a one-dimensional (1-D) search of a concentra ted cost function.