Video-SAR using higher order Taylor terms for differential range

The backprojection algorithm has several advantages over Doppler based synthetic aperture radar (SAR) image formation. These advantages have made it a standard choice for video-SAR, where measurements from airborne radars are continuously received and processed into imagery. Backprojection provides higher fidelity throughout the entire image, has greater flexibility of the image and flight path orientations, and is inherently immune to geometric distortions due to plane wave assumptions. Furthermore, the parallel nature of backprojection makes it ideally suited for implementation on general purpose graphical processing units (GPUs). However, GPUs are often designed for optimum single-precision performance and relatively slow double-precision performance. Backprojection relies on computing the differential range (ΔR) from every array position to every pixel, typically requiring a large number of double-precision operations. It has been suggested to exploit the first-order Taylor coefficients of ΔR, i.e., the far-field linear approximation, carried out using single-precision operations at the expense of significant image quality degradation. In this work we show that the single-precision, second-order Taylor approximation of ΔR yields a significant performance advantage over the double-precision square roots, while maintaining superior image quality. Geometric precision errors are estimated using third-order coefficients and verified numerically using simulations. SAR images are qualitatively compared using data collected by General Atomics Aeronautical Systems, Inc. (GA-ASI).