Abstract: A novel adaptive time delay estimation approach,referred to as CAED for short,is proposed based on covariation series because the impulsive noise may usually be modeled as α-stable distribution in the application.Firstly,the impulsive noise is removed and the mixed signal-to-noise ratio(MSNR) is improved by computing the cross-covariation between two received signals and the auto-covariation of one received signal with the information of the time delay still remaining.Secondly,the cross-covariation and auto-covariation series are regarded as time series and are put into two adaptive filters.The difference between the peak locations of two filter weight coefficients indicates the relative time delay between two received signals when they are convergent under the least mean square error criterion.Computer simulation studies show that the CAED algorithm gives an improved approach to estimating the time delay with α-stable noises under the lower MSNR.