Robust time-delay estimation in impulsive noise using ℓp-correlation

Time-delay estimation (TDE) is an important problem in radar target localization and range profile imaging. A common approach to TDE is matched filtering or equivalently cross-correlation, which is statistically optimal in white Gaussian noise. However, its performance greatly degrades in the presence of impulsive noise or non-Gaussian clutter. In this paper, a new concept called ℓ_p-correlation (0 <; p ≤ 2), which generalizes the conventional correlation from Hilbert space to the ℓ_p-space, is proposed. In addition, several important mathematical properties of the ℓ_p-correlation are given and proved. Based on the ℓ_p-correlation, a family of TDE algorithms robust against heavy-tailed noise or clutter are developed. Simulation results under a-stable noise are provided to demonstrate its robustness and accuracy.