A Robust PAST-Based ESPRIT Algorithm with Variable Forgetting Factor and Regularization for Frequencies/Harmonics Estimation in Impulsive Noise

Abstract

The estimation of signal parameters via the rotational invariance techniques (ESPRIT) algorithm is an efficient method for frequency estimation, and it has many applications in power signal analysis. As ESPRIT estimates the signal subspaces and frequency through the eigenvalue problem, it poses significant arithmetic complexity in real-time applications. This article proposes a robust recursive ESPRIT algorithm with variable forgetting factor (VFF) and variable regularization (VR) for online frequencies/harmonics estimation. The algorithm is based on the projection approximation subspace tracking method. Moreover, the locally optimal FF (LOFF) scheme is incorporated to improve its convergence performance and estimation precision. Furthermore, the estimation variance in signal fading scenarios is reduced with the use of the VR scheme. To improve the robustness against the possible impulsive noise encountered in power signals, a robust statistics-based M-estimate objective function is employed to suppress the adverse effect. The asymptotic convergence of the proposed robust algorithm is studied using the ordinary differential equation method. Simulation results on synthetic, stimulated wind turbine and electric arc furnace measurement data demonstrate that the proposed robust LOFF-VR recursive ESPRIT algorithm performs better than the conventional sliding window and constant FF methods both in stationary and nonstationary environments, especially during signal fading and impulsive noise scenarios. Specifically, the mean absolute percentage error (MAPE) of the estimated frequency measurements obtained by the proposed approach in moderately separated two tones scenarios at a 30-dB signal-to-noise ratio (SNR) is around 0.00030%, considerably smaller than other methods tested.