  Unmanned aerial vehicles (UAV) often rely on GPS for navigation. GPS signals,
however, are very low in power and easily jammed or otherwise disrupted. This
paper presents a method for determining the navigation errors present at the
beginning of a GPS-denied period utilizing data from a synthetic aperture radar
(SAR) system. This is accomplished by comparing an online-generated SAR image
with a reference image obtained a priori. The distortions relative to the
reference image are learned and exploited with a convolutional neural network
to recover the initial navigational errors, which can be used to recover the
true flight trajectory throughout the synthetic aperture. The proposed neural
network approach is able to learn to predict the initial errors on both
simulated and real SAR image data.
