Statistics of SAR Interferograms with Application to Moving Target Detection

Abstract : This report examines the statistics of the phase and magnitude of SAR interferograms towards the deployment of along-track interferometry (ATI) for slow ground moving target indication (GMTI). Great importance is attached to the practical applicability of the derived theoretical results, particularly with regard to the experimental MTI-mode of Radarsat2. Therefore, the results are evaluated with experimental airborne SAR data acquired during flight trials conducted in Petawawa in 1999. While the known probability density function (pdf) of the interferogram's phase (derived under the assumption of Gaussian backscatter) is shown to agree almost perfectly for a wide variety of backscatter conditions, the corresponding magnitude's pdf tends to deviate strongly in most cases. Motivated by this discrepancy, a novel distribution is derived for the interferogram's magnitude. This pdf, called the polynomial or p-distribution, matches the real data much more accurately, particularly for extremely heterogeneous composite terrain. Based on these statistics, a completely automatic detection scheme with constant false alarm rates for slow moving targets is proposed. All involved parameters required to determine the detection thresholds are estimated from the sample data. It is demonstrated on the basis of a real SAR scene that this detector is capable of detecting slow moving vehicles within severe ground clutter. Finally, practical aspects of the implementation and numerical stability are addressed, since many of the functions involved are comprised of indefinite power series which have to be handled cautiously.