Differencing Methods for 3D Positioning of Spacecraft

In this paper we describe the methods and system concepts that detect and locate in real-time the active (cooperative) and passive (non-cooperative) spacecraft, which we call targets, at the Geostationary Orbit (GEO) and at lunar distances. The methods do not assume any orbital knowledge of the target spacecraft, thus can be used for both quiescent and maneuvering spacecraft. We show by simulations that this approach can achieve meter-level three-dimension (3D) positioning accuracy with reasonable time delay measurement accuracy. The methods leverage on existing satellites and natural features (lunar case) with accurately known positions that can act as references, and/or in the case of the GEO places a dedicated "reference" spacecraft into an eccentric geosynchronous orbit over a region of interest (e.g., sky above North America). The ground antennas track the signals transmitted or reflected by the target and the reference spacecraft to measure their signals' time difference of arrival (TDOA). There are two modes of operations: "Single-differencing" - this approach assumes a transmitting radar illuminating both the reference and an uncooperative spacecraft (the target), and the ground radar antennas receiving the radar echoes to derive the relative position between the reference and the target. Double-differencing - this approach applies to the scenarios when either (a) the target and/or the reference spacecraft with difference clocks transmitting one-way ranging signals to the ground, or (b) multiple uplink radars are used to illuminate the reference and the target. We outline the mathematical derivations of the above schemes, and provide the accuracy performance simulations for some realistic and hypothetical scenarios. We also discuss some other applications.