Robust Time Delay Estimation Based on Sigmoid Transform in the Presence of Impulsive Noises

Abstract

A large class of physical phenomenon observed in practice exhibits impulsive, which can be modeled as alpha-stable distribution. Although methods based on fractional lower-order moments (FLOMs) have proven successful in dealing with non-Gaussian impulsive processes, they require in general the previous knowledge or estimation of characteristic exponent in order to choose an appropriate parameter value. In this paper, based on sigmoid transform, a robust approach for time delay estimation (TDE) is introduced in the presence of impulsive noise, referred to as sigmoid cross-correlation (SCC). Compare with algorithms based on FLOMs, the SCC method needs not to choose any parameter and is used under any characteristic exponent. The reason for the robustness of the SCC algorithm under the lower order alpha-stable noise condition is that sigmoid function transforms the lower order alpha-stable process into a second order alpha-stable process. Simulation studies show the novel method is robust for very impulsive environments