Robustness analysis of music and esprit frequency estimators for sinusoidal signals with time-varying amplitude

In this paper, we address the problem of estimating the frequency of a sinusoidal signal with random, lowpass amplitude. We propose to use MUSIC and ESPRIT frequency estimators as if the signal had a constant amplitude. The aim of the paper is to analyze the degradation of performance induced by the aforementioned mismodelling. Unified expressions for the bias and variances of the MUSIC and ESPRIT frequency estimators are derived under the hypothesis of small bandwidth of the signal envelope. Numerical simulations illustrate the agreement between theoretical and empirical results and study the influence of the envelope bandwidth onto the frequency estimation performance.