A novel robust adaptive time delay estimation method

Based on zero-order statistics (ZOS), two robust adaptive approaches for time delay estimation (TDE) are introduced in the presence of impulsive noise, referred to as ZOSTDE and NZOSTDE. Through a logarithmic transform, the impulsive signals without finite variance become the logarithmic-order signals. In this case, all of the moments are finite. The ZOSTDE and NZOSTDE algorithm consider this property and the concept of geometric power, then the FIR filter models the two received signals added impulsive noises and its coefficients can be adaptive obtained under least mean square (LMS) error criterion in the logarithmic domain. Accordingly, the estimation of time delay between the two sources is the time index of the maximum in the coefficients. They overcome several shortcomings of algorithms using fractional lower-order moment. Simulation studies show they are robust for very impulsive environments.