Precise Distributed Satellite Navigation: Differential GPS with Sensor-Coupling for Integer Ambiguity Resolution

Precise relative navigation is a critical enabler for distributed satellites to achieve new mission objectives impossible for a monolithic spacecraft. Carrier phase differential GPS (CDGPS) with integer ambiguity resolution (IAR) is a promising means of achieving cm-level accuracy for high-precision Rendezvous, Proximity-Operations and Docking (RPOD), In-Space Servicing, Assembly and Manufacturing (ISAM) as well as satellite formation flying and swarming. However, IAR is extremely sensitive to received GPS signal noise, and may fail in adverse environments with severe multi-path or high thermal noise. This paper proposes a sensor-fusion based approach to achieve IAR under such conditions in two coupling stages. A loose coupling stage efficiently fuses through an Extended Kalman Filter the CDGPS measurements with on-board sensor measurements such as range from inter-satellite cross-links, and vision-based bearing angles from a monocular camera. A second tight-coupling stage augments the cost function of the integer weighted least-squares minimization with a soft constraint function using noise-weighted observed-minus-computed residuals from these external sensor measurements. Integer acceptance tests are empirically modified by a coefficient reflecting the added constraints. Partial ambiguity resolution is applied to graduate integer fixing, where a subset of ambiguities that maximizes the probability of success is selected for fixing rather than the full batch of ambiguities. These proposed techniques are packaged into flight-capable software, with ground truths simulated by the Stanford Space Rendezvous Laboratory’s ${{\mathcal{S}}^3}$ library using state-of-the-art force modelling with relevant sources of errors, and validated in two scenarios: (1) a high multi-path scenario involving rendezvous and docking in low Earth orbit, and (2) a high thermal noise scenario relying only on GPS side-lobe signals during proximity operations in geostationary orbit. This study demonstrates successful IAR in both cases, using the proposed sensor-fusion approach, thus demonstrating potential for high-precision state estimation under adverse signal-to-noise conditions.