Dynamic observability analysis for attitude, angular velocity, shape, and surface parameters

This paper discusses a dynamic observability analysis for attitude, angular velocity, shape, and surface parameters of Space Objects (SOs) using non-resolved images or light curve measurements. The Fisher information matrix and Cramér-Rao lower bound are introduced for calculating the observability of parameters used in SO models. Light curve measurements are known to be functions of SO rotational states, shape geometry, and surface parameters. This dependency is captured in the bidirectional reflectance distribution functions models. The rotational dynamics of SOs can be difficult to model due to the fact that external and/or control torques are unknown. This work assumes that these torques are known, and under this assumption dynamic observability is analyzed. An illustrative two-dimensional example is considered. This example consists of a simplified system with one angle and one angle rate to model the rotational dynamics of the SO. The Cramér-Rao lower bound is used to study the effects of geometry on estimation performance. It was found that as the number of sides increases, and the SO shape tends to an axially symmetric one, the observability in the attitude estimates are lost. Finally, the Cramér-Rao lower bound is compared with actual performances from estimation approaches for estimating the attitude of an SO.