Interpolation Kernels for Synthetic Aperture Sonar Along-Track Motion Estimation

The formation of high-resolution synthetic aperture sonar (SAS) imagery requires accurate estimates of the sensor's trajectory. This is frequently accomplished using the displaced phase center antenna technique, which utilizes cross correlation of the signals received on successive pings. Accurate estimates of the sensor's ping-to-ping advance are then made by measuring the along-track spatial coherence of the scattered field. Unbiased advance-per-ping estimates require an accurate model for the spatial coherence of the scattered field. This model may be found by the application of the van Cittert-Zernike theorem to the problem of pulsed active sonar systems. In this paper, it is shown that the spatial coherence for a typical high-frequency SAS collection geometry is well approximated by a Gaussian whose width is proportional to the sensor's element size. Gaussian and quadratic along-track interpolation kernel performances are compared for a pair of at sea data collections. A relative image quality metric, based on image contrast, is defined to quantitatively assess the performance of the pair of interpolation kernels. In both tests, the use of an along-track estimator is shown to provide improved image quality. Also in both tests, the performance of the Gaussian kernel exceeds that of the quadratic kernel.