Opportunities to use synthetic aperture radar (SAR) in scientific studies and military operations are expanding with the development of small SAR systems that can be operated on small unmanned air vehicles (UAV)s. While the nimble nature of small UAVs make them an attractive platform for many reasons, small UAVs are also more prone to deviate from a linear course due autopilot errors and external forces such as turbulence and wind. Thus, motion compensation and improved processing algorithms are required to properly focus the SAR images. The work of this dissertation overcomes some of the challenges and addresses some of the opportunities of operating SAR on small UAVs. Several contributions to SAR backprojection processing for UAV SARs are developed including: 1. The derivation of a novel SAR backprojection algorithm that accounts for motion during the pulse that is appropriate for narrow or ultra-wide-band SAR. 2. A compensation method for SAR backprojection to enable radiometrically accurate image processing. 3. The design and implementation of a real-time backprojection processor on a commercially available GPU that takes advantage of the GPU texture cache. 4. A new autofocus method that improves the image focus by estimating motion measurement errors in three dimensions, correcting for both amplitude and phase errors caused by inaccurate motion parameters. 5. A generalization of factorized backprojection, which we call the Dually Factorized Backprojection method, that factorizes the correlation integral in both slow-time and fast-time in order to efficiently account for general motion during the transmit of an LFM-CW pulse. Much of this work was conducted in support of the Characterization of Arctic Sea Ice Experiment (CASIE), and the appendices provide substantial contributions for this project as well, including: 1. My work in designing and implementing the digital receiver and controller board for the microASAR which was used for CASIE. 2. A description of how the GPU backprojection was used to improved the CASIE imagery. 3. A description of a sample SAR data set from CASIE provided to the public to promote further SAR research.

Factorized backprojection is a processing algorithm for reconstructing images from data collected by synthetic aperture radar (SAR) systems. Factorized backprojection requires less computation than conventional time-domain backprojection with little loss in accuracy for straight-line motion. However, its implementation is not as straightforward as direct backprojection. Further, implementing an azimuth window has been difficult in previous versions of factorized backprojection. This thesis provides a new, easily parallelizable formulation of factorized backprojection designed for both pulsed and linearly frequency modulated continuous wave (LFM-CW) stripmap SAR data. A method of easily implementing an azimuth window as part of the factorized backprojection algorithm is introduced. The approximations made in factorized backprojection are investigated and a detailed analysis of the corresponding errors is provided. We compare the performance of windowed factorized backprojection to direct backprojection for simulated and actual SAR data.