ℓ1-norm based nonparametric and semiparametric approaches for robust spectral analysis

The problem of frequency estimation can be solved by parametric, non-parametric or semi-parametric methods. The representative nonparametric and semiparametric methods, namely, iterative adaptive approach (IAA) and sparse learning via iterative minimization (SLIM) have been recently proposed. Since both of them are not robust to impulsive noise, their extensions, ℓ₁-IAA and ℓ₁-SLIM are derived to provide accurate spectral estimation in the presence of the heavy-tailed noise in this paper. In our study, the nonlinear frequency estimation problem is mapped to a linear model whose parameters are updated according to the ℓ₁-norm and iteratively reweighted least squares. Simulation results are included to demonstrate the outlier resistance performance of the proposed algorithms.