The group delay of the Archimedean-spiral antenna was cataloged into the dispersion part and the constant part. Then a geometrical analysis was used to reveal the inherent dispersion property of the antenna's group delay. As a result, it effectively compensated the unknown antenna with its geometry measured. The constant group delay of the antenna was added into the system delay as a whole, and the whole delay was estimated through the Hough transformation of the hyperbola of a calibration marker (e.g. trihedral), as one of the curve parameters is the system delay. By an estimation of the azimuth location of the nadir of the curve using its symmetrical property, the dimension of the Hough transformation is further eliminated, so the method is efficient. Rail Ultra Wide Band SAR (UWB-SAR) data processing result verified the compensation method.