Robust relative navigation for spacecraft rendezvous using differential drag

Abstract

This work is concerned with the development of relative navigation filters processing relative position measurements of two satellites that perform rendezvous via differential drag only along low Earth orbits. The filters are developed in the Leader Hill frame with an emphasis on differential drag uncertainty modeling. Embedding the atmosphere density daily high variability in a bitopic uncertainty yields a novel robust H∞ filter of the six relative motion states. For comparison two Kalman filters matched to other atmosphere density models are developed. Furthermore the navigation are embedded in a realistic guidance navigation and attitude control and determination architecture (GNC/ADC) for nanosatellites. The proposed test case features two nanosatellites at 300 km altitude switching from positive to negative differential drag modes via 3D rigid body rotation. The 3D attitude control system involves three reactions wheels and three magnetorquers. The satellites inertial attitudes are estimated using three rate gyroscopes and coarse vector measurements. The proposed GNC/ADC scheme is tested in a high fidelity simulation environment. With 1 m relative position measurement accuracy and 10° attitude pointing accuracy the steady-state along track navigation errors are 4 m, 7 m, and 8 m (RMS) for the H∞ filter and the Kalman filters, respectively. The H∞ filter also shows quicker convergence and lesser sensitivity to the atmosphere density high variability. The two satellites succeed in closing an initial along track separation distance from 7500 m down to 250 m within 10 orbits, while the final radial deviation is about 10 m.