Anti-Temporal-Aliasing Constraints for Image-Based Feature Tracking Applications With and Without Inertial Aiding

Image-aided navigation techniques can determine the navigation solution (position, velocity, and attitude) by observing a sequence of images from an optical sensor over time. This operation is based on tracking the location of stationary objects in multiple images, which requires solving the correspondence problem. This paper enhances previous research efforts to characterize the correspondence problem using fundamental optical principles and statistical temporal sampling theory by including a rigorous derivation of the Nyquist constraint in pixel space. This development results in a general temporal sampling constraint and reveals the essential connection between the deleterious effects of temporal aliasing and the ambiguities that plague the correspondence search problem. This temporal image sampling constraint is expressed as a function of the navigation trajectory for elementary camera motions. The predicted temporal sampling (also known as frame) rates are on the order of those needed for adaptive optics control systems and require very large bandwidths. The temporal image sampling constraint is then reevaluated by incorporating inertial measurements. The incorporation of inertial measurements is shown to reduce the required temporal sampling rate to practical levels, which evidences the fundamental synergy between image and inertial sensors for navigation and serves as the basis for a real-time adaptive antialiasing strategy.