An adaptive, non-singular measurement model for angles-only orbit determination and estimation

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 which may introduce singularities. 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. The new adaptive measurement model is used in an orbit determination framework based on Gaussian least squares differential correction (GLSDC) and an online extended Kalman filter (EKF). A modified version of the Herrick-Gibbs method that incorporates the static form of the measurement model is used as a “warm start” to initiate the estimation scheme. Two scenarios are presented: (1) a small number of observers tracking a single target, and (2) a large constellation of observers 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.