Relative Orbital Element Estimation and Observability Analysis for Formation Flying Satellites using Inter-Satellite Range Measurements Only

This paper investigates to what extent the relative orbital elements of two satellites flying in formation can be estimated making use of inter-satellite range measurements only. Since the determination of relative orbital elements does not require the orientation of the relative orbit with respect to absolute inertial space to be resolved, as would be the case for absolute orbital elements, the question arises whether relative range measurements alone can be sufficient to solve the problem of interest. Providing an answer to this question is both of academic and practical interest, especially for formation flying missions utilizing very small satellites that are limited in their capabilities. To this end, a linearized relative dynamics model is implemented using an iterative batch least-squares algorithm to estimate rectilinear relative positions and velocities, which are subsequently converted to relative orbital elements for a number of test cases. Furthermore, the observability of the system is analyzed to investigate which relative orbital elements are most observable