Semi-Analytic Approach to Rapid Orbit Determination for the Perturbed Two-Body Problem
Open Access
- Author:
- Cope, Erin
- Graduate Program:
- Aerospace Engineering (MS)
- Degree:
- Master of Science
- Document Type:
- Master Thesis
- Date of Defense:
- July 07, 2023
- Committee Members:
- Amy Pritchett, Program Head/Chair
Puneet Singla, Thesis Advisor/Co-Advisor
Roshan Thomas Eapen, Committee Member
Robert G. Melton, Committee Member - Keywords:
- orbit determination
general perturbation theory
NORAD Elements
Astrodynamics
Conjugate unscented transform
statistical linearization
nonlinear least squares - Abstract:
- Ensuring a safe operating environment for existing and future space objects relies on maintaining a catalog of existing resident space objects. As the number of space objects increases, it is imperative to improve the accuracy and computational efficiency of algorithms tasked to update the catalog periodically. Traditionally, this update has been done by processing measurements of the space objects using optical or radar sensors and incorporating simplified dynamical models to perform orbit determination. While optical sensors routinely provide angles-only data, traditional algorithms for orbit determination depend on methods that approximate the nonlinear dynamics of resident space objects. The goal of this thesis is to develop tools to incorporate information from the nonlinear dynamics while keeping the implementation of these orbit determination methods computationally tractable. Specifically, this thesis proposes to combine advancements in semi-analytic satellite theory with statistical methods to accurately compute a direct mapping between the NORAD elements and the state space in a derivative-free manner. This mapping is obtained using a set of orthogonal basis functions to create a polynomial model of the dynamics that relates a space object’s state vector, as taken from the object’s most recent catalog data (NORAD elements), to the object’s position at the epoch of the measurement. The coefficients of these polynomials are found through the application of a non-product quadrature rule known as the conjugate unscented transform. The result is a larger domain of validity as compared to traditional methods of numerically propagating state transition matrices. This mapping is then incorporated directly within a non-linear least squares regression routine for orbit determination. The results of this regression are validated across various orbit regimes for multiple measurement models.