ℓp-norm based iterative adaptive approach for robust spectral analysis

•A generalized iterative adaptive approach (IAA) is proposed for robust spectral analysis.•A weighted ℓp-normℓp-norm is exploited to achieve higher accuracy and outlier resistance.•Its estimation performance is superior to original IAA in impulsive noise.

Recently, the iterative adaptive approach (IAA) has been shown to be an effective nonparametric methodology for high-resolution spectral analysis. Its main idea is to reformulate the nonlinear frequency estimation problem as a linear model whose parameters are updated iteratively according to weighted least squares. Since the derivation of the IAA is based on ℓ2-normℓ2-norm, it cannot work properly in heavy-tailed noise environment. In this paper, a generalized version of IAA is derived to provide accurate spectral estimation in the presence of impulsive noise, which replaces the ℓ2-normℓ2-norm by the ℓp-normℓp-norm where 1