An improved LS algorithm for the estimation of an impulsive noise corrupted signal by linear programming

Least squares (LS) algorithms are often used in many spectrum estimation methods. However, when the signals are contaminated by a few strong noise spikes, the standard LS algorithm can easily lead to biased solutions characterized by a strongly reduced dynamic range of the estimated spectra. In order to treat this problem, the classical approach is to weight the prediction errors before applying the LS minimization algorithm. In the present work a procedure for assigning optimal weights to the prediction equations is presented. The set of weights is computed, by linear programming techniques, in order to reduce the effects of strong impulsive noise. In order to demonstrate the capability of the proposed approach, the algorithm has been tested with signals corrupted by stationary white noise, impulsive additive spikes, and a combination of both. The results show a high degree of robustness that makes the method attractive for automatic analysis of real-world data.