Space object translational and rotational state prediction and sensitivity calculation




Hatten, Noble Ariel

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While computing power has grown monumentally during the space age, the demands of astrodynamics applications have more than kept pace. Resources are taxed by the ever-growing number of Earth-orbiting space objects (SOs) that must be tracked to maintain space situational awareness (SSA) and by increasingly popular but computationally expensive tools like Monte Carlo techniques and stochastic optimization algorithms. In this dissertation, methods are presented to improve the accuracy, efficiency, and utility of SO state prediction and sensitivity calculation algorithms. The dynamical model of the low Earth orbit regime is addressed through the introduction of an upgraded Harris-Priester atmospheric density model, which introduces a smooth polynomial dependency on solar flux. Additional modifications eliminate singularities and provide smooth partial derivatives of the density with respect to SO state, time, and solar conditions. The numerical solution of the equations of motion derived from dynamics models is also addressed, with particular emphasis placed on six-degree-of-freedom (6DOF) state prediction. Implicit Runge-Kutta (IRK) methods are applied to the 6DOF problem, and customizations, including variable-fidelity dynamics models and parallelization, are introduced to maximize efficiency and take advantage of modern computing architectures. Sensitivity calculation -- a necessity for SSA and other applications -- via RK methods is also examined. Linear algebraic systems for first- and second-order state transition matrix calculation are derived by directly differentiating either the first- or second-order form of the RK update equations. This approach significantly reduces the required number of Jacobian and Hessian evaluations compared to the ubiquitous augmented state vector approach for IRK methods, which can result in more efficient calculations. Parallelization is once again leveraged to reduce the runtime of IRK methods. Finally, a hybrid special perturbation/general perturbation (SP/GP) technique is introduced to address the notoriously slow speed of fully coupled 6DOF state prediction. The hybrid method uses a GP rotational state prediction to provide low-fidelity attitude information for a high-fidelity 3DOF SP routine. This strategy allows for the calculation of body forces using arbitrary shape models without adding attitude to the propagated state or taking the small step sizes often required by full 6DOF propagation. The attitude approximation is obtained from a Lie-Deprit perturbation result previously applied to SOs in circular orbits subject to gravity-gradient torque and extended here to SOs in elliptical orbits. The hybrid method is shown to produce a meaningful middle ground between 3DOF SP and 6DOF SP methods in the accuracy vs. efficiency space.


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