Demonstration of Adaptive Extended Kalman Filter for Low Earth Orbit Formation Estimation Using CDGPS

Carrier-phase Di®erential GPS is an ideal sensor for formation °ying missions in low Earth orbit since it provides a direct measure of the relative positions and velocities of the vehicles in the °eet. This paper presents results for a relative navigation ̄lter that achieves centimeter-level precision using measurements from a customized GPS receiver. This work uses a precise, robust extended Kalman ̄lter that is based on relatively simple measurement models and a linear Keplerian propagation model. To increase the robustness of the ̄lter in the face of environment uncertainty, the ̄lter is adapted using MMLE algorithms. The adaptive ̄lter is used to accurately identify the process noise and sensor noise covariance for the system. Despite the simplicity of the ̄lter, hardware-in-the-loop simulations performed on the Formation Flying Testbed at the Goddard Space Flight Center demonstrate that this ̄lter can achieve 1⁄42 cm relative position accuracy and <0.5 mm/s relative velocity accuracy for a range of Low Earth Orbit formations. Presented at the Institute of Navigation GPS Meeting, Portland OR, September 2002 INTRODUCTION Orbital relative navigation is a critical technology for a range of orbital formation °ying missions. NASA, the Department of Defense (DoD), and the European Space Agency (ESA), are all currently planning low Earth orbit (LEO) formation °ying missions [1, 2]. Some of these missions, such as TechSat-21, require relative navigation accuracy on the order of 2 cm position for separations of several kilometers. The goal of this research has been to develop a relative navigation sensor that can meet these requirements in real-time. Carrier-phase Di®erential GPS provides an ideal sensor to deliver the required performance. It can be relatively low cost, and it is reliable and robust. It also has a four-in-one sensor capability, with the ability to deliver absolute state, relative state, time, and attitude sensing. GPS has already been demonstrated many times for absolute navigation on orbit [3]. (The absolute state refers to the state with respect to the center of the Earth. The relative state refers to the state of an individual vehicle with respect to some point local to the formation.) GPS has also been used onorbit for relative navigation [3, 4, 5]. However, the actual relative navigation performance achieved on these missions is not su±cient. The best results from actual °ight data has been 8-10 meters position accuracy, and about 1 cm/s velocity accuracy. To improve this, there have already been 2-vehicle hardware-inthe-loop relative navigation demonstrations using carrier di®erential GPS with signi ̄cantly better performance. Binning used a dual frequency TurboRogue receiver and the Naval Research Laboratory's OCEAN orbital model to achieve 15cm relative position and 0.3 mm/s relative velocity accuracy [6]. Ebinuma used a simpler single-frequency receiver in closed-loop rendezvous simulations, and demonstrated 5 cm position accuracy and 1 mm/s velocity accuracy [7]. More recently, we have reported results from decentralized 4-vehicle formation hardware-in-the-loop simulations also using a single-frequency receiver [9]. For 1 km separations, relative position accuracy of 1cm and velocity accuracy of 0.3 mm/s was demonstrated.