Robust Spectral Analysis of Multi-Channel Sinusoidal Signals in Impulsive Noise Environments

Robust spectral analysis of the sinusoidal signals corrupted by impulsive noise poses a big challenge in the signal processing community. In this paper, we address the issue of robust spectral analysis for multi-channel sinusoidal signals, including order detection and parameter estimation. The successive robust low-rank decomposition is firstly designed to extract the common signal subspace from the multi-channel data matrix. Subsequently, the number of sinusoidal poles is determined with a model order selection criterion, based on the so-obtained subspace. With the signal order information, the sinusoidal parameters and outliers are jointly estimated according to the maximum a posteriori criterion. To find a robust initial guess of the sinusoidal parameters, an estimator based on robust weighted linear prediction is developed. Additionally, the performance analysis is provided, which includes computational complexity, convergence verification of the sinusoidal parameter estimation, and asymptotic consistency of the signal order detection. Simulation results demonstrate the advantages of the proposed robust spectral analysis framework compared to state-of-the-art schemes.