Necessary and Sufficient Conditions for Attitude Estimation in Fractionated Spacecraft Systems

This paper addresses the problem of attitude estimation in fractionated spacecraft clusters. Each module in the cluster may have either a star-tracker, a relative attitude sensor, or both. Using results in nonlinear ob- servability theory, we provide graph-theoretic sufficient conditions for the attitude of every module to be observable. In particular we show that the attitude of every module in the cluster can be observed if every module has either a star tracker with non-collinear stars, or there is a path through the sensing network from a module with a star tracker to the module without a star tracker, and each of the relative measurements along the path has either multiple non-collinear beacons or a single beacon that is not parallel to the rotation vector of the target module.