Robust Frequency Estimation in Symmetric $$\alpha $$-Stable Noise

The symmetric \(\alpha \)-stable (S\(\alpha \)S) noise is commonly encountered in a variety of applications such as wireless communications and image processing. In this work, combining the linear prediction property and \(\ell _p\)-norm minimization, a robust frequency estimator is devised for a complex sinusoid in the presence of the S\(\alpha \)S noise. The proposed algorithm, based on the \(\ell _p\)-norm of the preprocessed linear prediction errors, can be regarded as the outlier-resistant version of the generalized weighted linear prediction frequency estimation approach. Computer simulations are conducted to contrast the performance of the proposed algorithm with three conventional frequency estimators. The results indicate that our method is robust to outliers and nearly optimal compared with Cramer–Rao lower bound.