Separating Attitude and Shape Effects for Non-resolved Objects

Abstract

Radiometric measurements provide a means of constraining the attitude and/or shape of on-orbit objects that are too small or distant to be imaged by ground-based optical or radar facilities. At the most general level, a detailed analysis of radiometric data to determine attitude and shape entails the numerical inversion of a multivariate integral equation involving two classes of variables: “attitude” and “body” parameters. Attitude parameters specify the object orientation at the times of the observations and provide a means to convert between the inertial reference frame and the body-fixed reference frame. Body or “shape” parameters provide the information required to calculate the radiant intensity of the object from within the body-fixed reference frame. Our analysis indicates that the most basic requirement for the analysis is an extensive set of radiometric observations, ideally gathered from multiple perspectives and under multiple illumination conditions. Given such a rich data set, a complete attitude/shape inversion analysis requires supercomputer resources to address in a timely fashion, even for relatively simple convex objects. The basic reason for this is that the inversion approach requires solving for a large number of object attitude and shape parameters. A significantly more computationally efficient means of addressing the problem would be to separate the attitude and body parameter determination analyses, if at all possible. To this end, we present a variety of theoretical approaches for both shape-independent attitude analysis and attitudeindependent shape analysis for non-resolvable objects.