James Hippelheuser, University of Central Florida; Tarek Elgohary, University of Central Florida
Keywords: Space Situational Awareness, Line of Sight, Orbit Estimation, Initial Orbit Determination, Angles Only Measurements
Abstract:
Within this work, a new adaptive measurement model is adopted for orbit determination and estimation. The new measurement model revolves around a network of observation nodes that utilizes angle-only line-of-sight measurements produced by a monocular camera. The line-of-sight measurements from each observation node are used to define a pair of orthogonal geometric planes that intersect both the observation node and the target. The intersection of these geometric planes defines the line between each observation node and the target within the inertial frame. This results in three possible combinations of the components of the line-of-sight vector, each of which involves a matrix inversion operation. Therefore, a singularity may exist in the event that the relative position unit vector between an observer and the target becomes two dimensional, which has to be accounted for. Previously, this measurement model has been used to demonstrate a network of space-based observation satellites to track an object in orbit. Only one of the possible measurement models was used. The results from the previous scenarios demonstrate that the measurement model can produce accurate orbit estimation within the inertial frame. Whenever the measurement model approached the singularity, the solution was to remove the bad measurements from the estimation scheme for the period that the singularity existed. To that end, the per-observer instantaneous observability was used as a quantitative threshold for the quality of the measurements. In this work, we introduce an adaptive singularity free measurement model based on maximizing the determinant of the measurement matrix that leads to the optimal condition number. By selecting the line of sight components associated with the optimal solution, the measurement model is guaranteed to be singularity free. This in turn, results in better coverage of the target object by the constellation of observers and leads to a more robust overall measurement model at each time-step. The new adaptive measurement model is used in an orbit determination framework based on Gaussian least squares differential correction and an online extended Kalman filter. A modified version of Herrick-Gibbs method that incorporates the static form of the measurement model is used as a warm start to initiate the estimation scheme. The two scenarios conceived are a small number of observers tracking a single target and a large constellation of observers capable of tracking a target within a range of orbits. The results show that the adaptive measurement model is capable of performing accurate orbit determination and estimation.
Date of Conference: September 14-17, 2021
Track: Astrodynamics