Robust Frequency Estimation of Multi-sinusoidal Signals Using Orthogonal Matching Pursuit with Weak Derivatives Criterion

In this paper, the weak derivatives (WD) criterion is introduced to solve the frequency estimation problem of multi-sinusoidal signals corrupted by noises. The problem is therefore modeled as a new least squares optimization task combined with WD. To overcome the potential basis mismatch effect caused by discretization of the frequency parameters, a modified orthogonal matching pursuit algorithm is proposed to solve the optimization problem by coupling it with a novel multi-grid dictionary training strategy. The proposed algorithm is validated on a set of simulated datasets with white noise and stationary colored noise. The comprehensive simulation studies show that the proposed algorithm can achieve more accurate and robust estimation than state-of-the-art algorithms.