A Nonlinear Least Squares Phasor Estimation Algorithm with a Trust Metric

Abstract

The paper presents a separable nonlinear least squares (NLLS)-based approach for estimation of fundamental-frequency phasors from sampled point-on-wave measurements. An analytical connection is established between the NLLS cost function and the discrete Fourier transform (DFT)-based periodogram of the input signal. This periodogram-based interpretation of the cost function offers an intuitive and easy-to-implement solution for the frequency estimate. Using the residual error of the NLLS-fit, the paper also presents an insightful measure for ascertaining the quality of the phasor estimates and their validity, especially for data windows containing signal transients.