Aiaa-98-4560 Autonomous Orbit Determination for Two Spacecraft from Relative Position Measurements

A batch filter has been designed and analyzed to autonomously determine the orbits of 2 spacecraft based on measurements of the relative position vector from one spacecraft to the other. This system provides a means for high-precision autonomous orbit determination for systems that cannot be dependent on signals from the GPS constellation or ground stations. The filter uses a time series of the inertiallyreferenced relative position vector, and it uses orbital dynamics models for the two spacecraft. It estimates the 6-element orbital state vectors of both spacecraft along with a drag parameter for each one. The observability of this system is demonstrated in this proof-of-concept study, and the filter’s predicted position determination accuracy is analyzed for a number of situations. Position accuracies on the order of 1 m RMS are predicted for certain configurations. Introduction Knowledge of orbit and position is a practical requirement for all Earth-orbiting spacecraft. Traditional methods of orbit determination rely on ground-based tracking measurements of range and range rate. Recently there has been much interest in techniques that are based on using signals from GPS receivers. More exotic methods have been proposed or developed that can determine a spacecraft's orbit autonomously, i.e., based solely on data from sensors that are on board the spacecraft. Some satellite systems have an autonomous orbit determination requirement that stems from military considerations. In the event of a war, ground-based or GPS-based orbit determination aids may be destroyed or their signals may be jammed. Therefore, there is a need for autonomous orbit determination capabilities beyond those that can be provided by an on-board GPS receiver. This paper analyzes an idea for autonomous orbit determination of Earth-orbiting spacecraft that was ∗ 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. first proposed and analyzed by Markley. The basic idea is to simultaneously determine the orbits of 2 spacecraft by making measurements of the vector from one spacecraft position to the other. In order to make the two orbits observable, this vector must be referenced to inertial space, and a time series of these measurements is needed. All of the sensors for the proposed system could reside on one of the spacecraft. Suppose that the instrumented spacecraft is called “Spacecraft A” and the other spacecraft is called “Spacecraft B.” Spacecraft A will need a 3-axis star sensor system to determine its inertial attitude. It will also need instrumentation to measure the position vector of Spacecraft B in its own spacecraft-fixed reference frame. Such instrumentation could consist of a laser range finder for measuring the distance to Spacecraft B and an optical telescope for measuring the direction to Spacecraft B. Spacecraft B could be a dumb drone, perhaps just a metal sphere with suitable reflective coating to reflect Spacecraft A’s laser range finder signal and to reflect enough sunlight to make it visible to Spacecraft A’s optical system. A number of other researchers have studied spacecraft-to-spacecraft range measurements to enhance orbit determination capabilities for a constellation of spacecraft. The orbits are not all independently observable because a simultaneous rigid-body-type motion of the entire constellation does not affect the measurements. These studies have focused on lowering the drift rates of the estimated orbits by using cross-link range data. Reference 11 considered many different measurement sets for autonomous orbit determination of high altitude spacecraft, including range and inertially-referenced angles from one spacecraft to another. The difference between that study and the present one is that Ref. 11 considered the second spacecraft, Spacecraft B, to have a known orbit and position. Markley, in the appendix of his paper, showed that the two orbits of the proposed system are absolutely observable except for certain special orbital configurations. One important unobservable case is that of two spacecraft in coplanar circular orbits with the same semi-major axis. His analysis considered