Effects of frequency-dependent attenuation on the performance of time delay estimation techniques using ground penetrating radar

In this paper, we investigate the effects of frequency-dependent attenuation on the performance of some time delay estimation techniques applied to ground penetrating radar (GPR) data. The signal model is based on a complex power law of frequency for dielectric permittivity which describes wave propagation using two parameters, the quality factor Q and the phase velocity at an arbitrary reference frequency V_r. Hence, the adopted 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, Q and the product Bτ 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. The bandwidth over which this approximation is reasonably accurate depends on the reference frequency and the quality factor of the medium. Then, we use this error to compensate for the bias introduced by the model mismatch with the aim of improving the estimates.