A Comparative Study of Kalman Filter Implementations for Relative GPS Navigation

Relative global positioning system (GPS) navigation is currently used for autonomous rendezvous and docking of two spacecraft as well as formation flying applications. GPS receivers deliver measurements to flight software that use this information to determine estimates of the current states of the spacecraft. The success of autonomous proximity operations in the presence of an uncertain environment and noisy measurements depends primarily on the navigation accuracy. This thesis presents the implementation and calibration of a spaceborne GPS receiver model, a visibility analysis for multiple GPS antenna cone angles, the implementation of four different extended Kalman filter architectures and a comparison of the advantages and disadvantages of each filter used for relative GPS navigation. A spaceborne GPS model is developed to generate simulated GPS measurements for a spacecraft located on any orbit around the Earth below the GPS constellation. Position and velocity estimation algorithms for GPS receivers are developed and implemented. A visibility analysis is performed to determine the number of visible satellites throughout the duration of the rendezvous. Multiple constant fields of view are analyzed and results compared to develop an understanding of how the GPS constellation evolves during the proximity operations. The comparison is used to choose a field of view with adequate satellite coverage. The advantages and disadvantages of the relative navigation architectures are evaluated based on a trade study involving several parameters. It is determined in this thesis that a reduced pseudorange filter provides the best overall performance in both relative and absolute navigation with less computational cost than the slightly more accurate pseudorange lter. A relative pseudorange architecture experiences complications due to multipath rich environments and performs well in only relative navigation. A position velocity architecture performs well in absolute state estimation but the worst of the four filters studied in relative state estimation.