Distributed Estimate Fusion Filter for Large Spacecraft Formations

Abstract

A communication-enabled distributed estimation system is developed for a spacecraft formation keeping application that requires only the transmission of local state estimates in a circular manner about the formation. Unknown maneuvers in the form of thrust commands are accounted for by modeling the maneuvers as process noise. Time delays are accounted for by storing previous estimates and associated covariance matrices. Results show that the resulting state estimates, while suboptimal, are conservative with respect to an equivalent Kalman filter. Monte Carlo simulations of the proposed estimator with a formation keeping controller in an eight spacecraft formation show that the formation exhibits good performance even in the presence of large time delays (20-30 s) in the communication subsystem. NASA is currently studying several large scale spacecraft formation missions, many to be flown at the Earth-Sun libration points. The location affords scientists a much clearer view of the universe, while also providing a convenient gravitational pull to be Earth following. The Micro-Arcsecond X-ray Imaging Mission (MAXIM) 1 is an X-ray interferometer composed of 33 spacecraft and will be able to image the event horizon of a black hole. The Terrestrial Planet Finder (TPF) 2 mission shall enable scientists to find and study extra-solar planets similar to our own. While several designs are currently under review, a TPF design by Lockheed Martin is composed of four, possibly six, free flying spacecraft which will function as an infrared interferometer. The Stellar Imager (SI) 3 mission postulates that stellar activity is key to understanding life in the universe. Specifically, SI is a large, space based UV optical sparse aperture telescope/Fizeau Interferometer designed to study the sun. The formation is designed to be flown at the Earth-Sun libration point, as is TPF. The science of SI requires a large array of satellites in an irregular placement in order to accomplish its goals. The combination of interferometry and large formations make these and similar future missions especially challenging. Interferometry missions are especially challenging due to the high tolerance requirements. Such missions are currently slated to employ a multiple resolution control architecture: conventional thrusters and RF range and bearing sensors are to be used for coarse spacecraft control, and laser sensors and adaptive optics will provide fine optical path control. 1, 3 The Autonomous Formation Flying Sensor (AFF) has been identified as a key component for coarse control of spacecraft formations. 4, 5 The AFF provides range and bearing measurements between spacecraft based on GPS technology. Large formations of spacecraft present interesting challenges to the scientific community including: low fuel usage control for given precision requirements, fleet estimation given limited sensor and communication resources, and accurate relative state tracking to reduce fuel in the presence of the other challenges. Developing scalable algorithm tools is critical to the success of these missions. Related work includes Ref. 6 in which the authors present the least squares fusion method for N Kalman filters in a batch method by combining all estimates at once. The method described in this paper fuses each estimate iteratively and can account for time delays in the communication subsystem in between iterations. Another benefit of fusing sequentially is that the intermediate results are valid state estimates and can be