Kohei Fujimoto (The University of Colorado at Boulder), Daniel J. Scheeres (The University of Colorado at Boulder)
Keywords: IOD, orbit determination
Abstract:
Initial orbit determination (IOD) of space debris is an important segment of space situational awareness and is often coupled with the problem of track correlation, since in order to determine the orbit of an observed object, multiple observations must be combined. It is generally uncertain, however, whether two arbitrary tracks are of the same object. Recently, Fujimoto and Scheeres have proposed a novel and rigorous track correlation and IOD technique where each observation is assigned an admissible region in state space based on some physical constraints. The relationship of two observations is then determined by finding whether these regions intersect via Bayes rule. In this paper, we propose a new application of this method to space-based observations. Preliminary results show robustness to classically singular geometries, such as GEO-on-GEO observations. Admissible regions were first proposed by Milani et al. for heliocentric orbits, and Tommei et al. expanded this concept to Earth orbiting objects. Maruskin et al. was first to introduce the concept of intersecting multiple admissible regions to correlate tracks and obtain an initial orbit estimate, albeit the correlation was conducted in 2-dimensional subspaces of the state space. Fujimoto and Scheeres fully developed ways of characterizing intersections of admissible regions in the full 6-dimensional state space. They showed through topological arguments that a positive correlation also simultaneously provides an initial orbit estimate. A method of linearly mapping admissible regions to the state space was introduced in order to improve computational turn-around, and was validated with a series of numerical tests. For space-based observations, the observation location vector, previously assumed to be Earth-fixed, is now allowed to propagate under two-body dynamics. Several technical challenges arise when we make this change. First, the admissible region spans over a larger region in the state space, making the correlation process more computationally intensive. Second, a modification must be made to the correlation process as the observer’s state is always a valid solution. That is, any admissible region map from a space-based observation will intersect with any other map from the same observing satellite at the observing satellite’s state. This problem is circumvented by automatically refining the state space discretization and throwing away solutions near the observing satellite’s state. Numerical examples for several observation scenarios are discussed in this paper, including LEO-on-GEO and GEO-on-GEO observations. The LEO satellite is in a circular sun-synchronous orbit at 630 km altitude, much like the SBSS System. For existing IOD techniques there are known observation geometries that experience singularities such as the GEO-on-GEO case. Preliminary results show that our method does not suffer such singularities for the GEO-on-GEO observation scenario. This outcome is most likely due to the fact that we are combining 2 observations for a total of 8 observable variables, instead of the minimum 6, to obtain an initial orbit estimate. We believe this additional information removes the singularity from the problem.
Date of Conference: September 13-16, 2011
Track: Poster