AIAA-98-4308 Autonomous LEO Orbit Determination From Magnetometer and Sun Sensor Data

A batch filter has been designed to autonomously estimate the orbit of a LEO spacecraft using data only from a magnetometer and a sun sensor. The goal of this study has been to prove the feasibility of a proposed low-cost, moderate-accuracy autonomous orbit determination system. The system uses a batch filter to estimate the Keplerian orbital parameters, a drag parameter, magnetometer biases, and corrections to the Earth's magnetic field. It does this by minimizing the square errors between measured and estimated values of two quantities, the Earth's magnetic field magnitude and the cosine of the angle between the sun vector and the Earth's magnetic field vector, both measured at the spacecraft. The proposed system is observable, and reasonable accuracy is obtainable. Given a magnetometer with a 10 nT 1-σ accuracy and a sun sensor with a 0.005 1-σ accuracy, the system can achieve 1-σ position accuracies on the order of 500 m for inclined LEO orbits. Introduction Knowledge of orbit and position is a requirement of virtually all spacecraft missions. There exist many orbit determination systems. Traditional systems rely on ground-based range and range-rate data to observe the orbit and position, as in Ref. 1. Autonomous orbit determination systems use only measurements that are available on board a spacecraft. References 2-9 discuss various autonomous orbit determination schemes. The GPS system provides the possibility of a semi-autonomous system. A spacecraft can determine its orbit solely from the positions and velocities that it gets from its GPS receiver. This is not truly autonomous because the spacecraft relies on signals from the GPS system. Different systems have widely different accuracy levels. Current ground-based systems can achieve position accuracies on the order of several centimeters. GPS-based systems can have position accuracies ranging from about 100 m down to 0.1 ∗ Associate Professor, Sibley School of Mechanical and Aerospace Engineering. Associate Fellow, AIAA. Copyright  1998 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. meter, depending on whether or not differential GPS is being employed or the GPS signal has been intentionally degraded for non-U.S.-military users. The truly autonomous systems advertise various levels of accuracy, ranging from 50 km down to 1 km or better. Many such systems have been studied only via simulation. Their true accuracies are not yet known. The aims of the present work are to prove the observability of a new autonomous spacecraft orbit determination system and to estimate its likely accuracy. The new system can operate in Low Earth Orbit (LEO). It uses only a 3-axis magnetometer and a sun sensor, both on-board the spacecraft. In addition to estimating the spacecraft's orbit, the system also estimates the magnetometer's biases and corrections to a model of the Earth's magnetic field. The proposed system is the latest in a sequence of systems that base their orbit determination capability on measurements of the Earth's magnetic field. The original idea, as introduced by Psiaki et al., was to compare on-board measurements of the Earth's magnetic field magnitude with a spherical harmonic model of that field. Any deviations were used to correct the orbit parameters. Using various filter designs, this basic system has been tested on flight data by Psiaki et al., Shorshi and Bar-Itzhack, and Wiegand. Achieved steady-state accuracies in these studies ranged from 8 km to 125 km. Accuracy was strongly influenced by the Earth field model's accuracy and by field measurement accuracy. Shorshi and Bar-Itzhack also tested a system that uses attitude data. It achieved accuracies on the order of 1035 km when tested with real flight data. Psiaki attacked the problem of inaccuracy in the Earth field model by developing a system that estimates corrections to this model while estimating the spacecraft orbit. In order to make the orbit and field model coefficients simultaneously observable, this system included a 3-axis star sensor in addition to a 3axis magnetometer. Simulation results predicted a system accuracy on the order of 300 m or better when using an accurate magnetometer and star sensor. The present work is an extension of the work of Ref. 7. The new idea is to replace the 3-axis star sensor with a sun sensor. This would make the system much more economical. In fact, many missions already include a sun sensor and a magnetometer for attitude determination and control purposes. If the presently-