The Effiency of Algorithms to match Unique Scatterer Locations in Joint 3D Azimuth and Elevation Synthetic Aperture Radar scenarios

Integral in locating point scatterers in Synthetic Aperture Radar (SAR) data is the ability to match location estimates in each dimension. This is due in some sense to the fact that the fundamental theorem of algebra finds unique locations only in one dimension. In SAR images this involves at least a search of four possible combination for two scatterers. In a set of multiple elevation SAR (3-D) images with more than one scatterer combinations increase dramatically. The paper examines several suboptimal methods and their efficiency matching scatterers in one or more dimensions to their unique locations compared to the (un-achievable) exhaustive search. Many heuristic methods exist in two dimension (location maxima, alternating maximization in each dimension) and some (radar tracking) methods exist in three dimensions (Munkres, probabilistic maximization). Algorithms range from simply selecting maximums (easy in 2D; complex in multiple images, 3D) to multidimensional constrained interpolations. In some algorithms the extra degrees of freedom present in two dimensional localization are exploited to increase accuracy. These methodologies can also be extended to three dimensions. The paper examines proposed combinations of these especially suitable to the 3-D SAR problem. Simulations with results for different algorithms compare promising alternatives to solve this problem.