Shambo Bhattacharjee, University of Leeds; John Kent, University of Leeds; Weston Faber, L3 Applied Defense Solutions; Islam Hussein, L3 Applied Defense Solutions; Moriba Jah, The University of Texas at Austin
Keywords: Uncertainty Propagation, point cloud, Adapted STructural (AST) coordinate system, Perturbation effects, Normality analysis
Abstract:
Consider a space object in an elliptical orbit about the earth. If the initial location and velocity, x(0) and v(0), are known 3-dimensional vectors at time t = 0, then the laws of Newtonian mechanics can be used to propagate the motion, i.e. to compute x(t) and v(t) for any t > 0. If the initial states are noisy, e.g. if the initial position and velocity are subject to isotropic normal errors, then a point cloud can be simulated at time t = 0 and followed through the time. Unfortunately, in the standard coordinate systems of astrodynamics (e.g. ECI, Keplerian and to some extent equinoctial) the representation of uncertainty can sometimes be extremely non-Gaussian. To solve this issue, we have recently introduced a new Adapted Structural (AST) coordinate system for the state vector, under which uncertainty is nearly Gaussian under a wide range of conditions (e.g. LEO vs. GEO; varying eccentricity, varying initial uncertainty; perturbations from Keplerian dynamics).
A Bayesian-type filter is easy to implement if the updated state vectors are normally distributed. Since AST coordinates are typically approximately multivariate normal after each update, a tracking algorithm such as the Unscented Kalman Filter (UKF) is appropriate. Most of our previous tests have been performed in ideal conditions, i.e, under Keplerian dynamics without incorporating any form of perturbation effects. Perturbation effects can be added using analytic approximations or by performing numerical integration. Analytic forms are easy to implement and computationally fast but generally not exact. On the other hand, numerical integration can provide an accurate solution but can be time consuming. In this paper, we extend the scope of AST coordinate system to include some perturbation effects, namely atmospheric drag and oblateness. We will assess the normality of the perturbed AST coordinates using statistical tests under various settings.
Date of Conference: September 11-14, 2018
Track: Astrodynamics