An ℓp-norm minimization approach to time delay estimation in impulsive noise

Estimating the time delay between two signals received at spatially separated sensors is an important topic in signal processing and has a variety of practical applications. Conventionally, time delay estimation (TDE) can be achieved in two steps. The coefficients of a finite impulse response filter used to model the subsample delay are first computed and then interpolated to produce the delay estimate. Despite its simplicity, the two-step method suffers from error accumulation, estimation bias, and is not robust to impulsive noise or outliers. To overcome these drawbacks, a family of robust algorithms for direct TDE is proposed using ℓp-norm minimization, with 1⩽p⩽2. Although the direct approach leads to a nonconvex optimization problem, efficient algorithms are designed for finding the global solution. Its robustness and accuracy in the presence of α-stable noise are demonstrated by comparing it with the standard two-step scheme, cross-correlator and fractional lower-order covariation method.