We present a high-SNR approach to estimating the orientation of distorted target objects, where the distortion is out-of-plane rotation. The presence and position of the targets are detected with a bank of distortion-invariant correlation filters. The filter set we use, known as hybrid composite filters, yields complex responses at the target locations. The peak magnitude responses indicate target locations. The correlation phase angles, at the target locations, are linearly combined into complex signatures unique to a particular orientation. A maximumlikelihood M-ary classification algorithm is used to determine the most likely orientation from a finite number of orientations. In practice, we do not use all the hybrid filters and the ones we do use are optimally selected and combined for detection and discrimination. Given the target location, additional filtering can be accomplished with an inner-product operation rather than correlation. A second set of filters, optimized for angle estimation, are applied as inner products at the target locations to construct the orientation signatures. A rigorous mathematical treatment of the optimum signature detection architecture is presented and numerical simulations demonstrate the capabilities of this approach.