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

Abstract

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 subspaces. 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.

Hybrid Deep Learning Framework for Reduction of Mixed Noise via Low Rank Noise Estimation

“…In order to estimate variance of AWGN, various blockbased and wavelet-based methods have been proposed [45], [46], [47], [48] where the variance is estimated by comparing the noisy image to the filtered image obtained by low pass filter to the noisy image. In recent years, low rank patchbased strategies for noise estimation have been proposed [49], [50], [51], [52]. It is worth noticing that the low rank approximation can also be effectively used to recover the underlying signal from the observed multi-channel data in the impulsive noise environments [52].…”

“…In recent years, low rank patchbased strategies for noise estimation have been proposed [49], [50], [51], [52]. It is worth noticing that the low rank approximation can also be effectively used to recover the underlying signal from the observed multi-channel data in the impulsive noise environments [52]. Inspired by these approaches, we exploited the principal component analysis (PCA) based mechanism described in [16] for noise estimation.…”

An Improved Toeplitz Approximation Method for Coherent DOA Estimation in Impulsive Noise Environments

“…The coherent DOA estimation methods mentioned above assume that ambient noise is Gaussian-distributed. In reality, however, there are various non-Gaussian noises with spike impulse characteristics [ 28 , 29 , 30 ], such as atmospheric noise, underwater noise, vehicle ignition, multi-user interference, etc. These impulsive noises usually have heavy-tailed distributions, which means the probability density function (PDF) decreases more slowly and outliers are more likely to occur compared to Gaussian distribution.…”