Effects of frequency-dependent attenuation on time delay estimation techniques applied to ground penetrating radar data

In this paper, the effects of frequency-dependent attenuation on the performance of some time delay estimation techniques applied to ground penetrating radar (GPR) data are investigated. Being based on a complex power law of frequency for dielectric permittivity, the adopted signal model deviates from the damped exponential model and it is this mismatch that is likely to deteriorate the performance of the employed techniques. At first, we carry out a sensitivity study by determining the variations of the relative root mean square error of the time delay estimates as a function of the SNR and the quality factor Q for three algorithms, namely, root-MUSIC, ESPRIT and the matrix pencil method (MPM). These variations reveal a systematic error which is quantified by means of a first-order approximation and is found to be the ratio of the phase delay to the group delay. Then, this error is used to compensate for the bias introduced by the model mismatch with the aim of improving the estimates.