A Study of Relative Space Navigation Incorporating Direct and Reflected GNSS Signals: Simulation and Analysis of Hubble Servicing Mission 4

When two spacecraft are docking, GNSS navigation of the controlled spacecraft is corrupted by GNSS signals reflected off the passive target spacecraft. Rather than treating these reflected signals, or multipath, as a source of error, they can be used as a source of information about the distance of the target from the receiver. This paper presents an analysis of receiver and target position estimation when reflected signal measurements are incorporated via a bistatic radar technique. Sequential estimation is performed with an Extended Kalman Filter using the Orbit Determination Toolbox, a mission simulation and analysis tool developed in MATLAB by engineers at Goddard Space Flight Center. Hubble Servicing Mission 4 is used as a case study. This is a simplified analysis of the actual scenario, assuming direct and reflected signals are separable and that pseudorange measurements can be made from each. The simulation nevertheless provides the opportunity to study the feasibility of incorporating reflected signals into a relative navigation solution during rendezvous and docking. The receiver and target initial state covariances necessary for convergence are studied and the influence of the target radar cross section is examined. The filter is shown to converge.