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Tombasco J.,University of Colorado at Boulder | Axelrad P.,University of Colorado at Boulder | Jah M.,U.S. Air force | Jah M.,Advanced science and Technology Research Institute for Astrodynamics
Journal of Guidance, Control, and Dynamics | Year: 2010

This study investigates dynamic modeling and orbit estimation of geosynchronous satellites using traditional and specialized orbit representations. Exact nonlinear variational equations for generally perturbed synchronous elements are developed via Poisson brackets. A hybrid element set is also introduced to avoid numerical sensitivities. Numerical propagation studies evaluate the precision and accuracy of inertial Cartesian, Keplerian, synchronous and hybrid element dynamic models. The suitability of approximating the synchronous element equations of motion for small eccentricity and inclination values is assessed. Results show that the hybrid and exact synchronous models are consistent for large and small time steps and are of comparable accuracy to the inertial Cartesian model. The hybrid element model is further validated via an estimation analysis that processes multiple nights of experimental optical data of the Tracking and Data Relay Satellite 8. The results show that the hybrid elements are suitable for geosynchronous dynamic modeling and estimation. Copyright © 2010 by the American Institute of Aeronautics and Astronautics, Inc.


Vishwajeet K.,State University of New York at Buffalo | Singla P.,State University of New York at Buffalo | Jah M.,U.S. Air force | Jah M.,Advanced science and Technology Research Institute for Astrodynamics
Journal of Guidance, Control, and Dynamics | Year: 2014

The main objective of this paper is to present the development of the computational methodology, based on the Gaussian mixture model, that enables accurate propagation of the probability density function through the mathematical models for orbit propagation. The key idea is to approximate the density function associated with orbit states by a sum of Gaussian kernels. The unscented transformation is used to propagate each Gaussian kernel locally through nonlinear orbit dynamical models. Furthermore, a convex optimization problem is formulated by forcing the Gaussian mixture model approximation to satisfy the Kolmogorov equation at every time instant to solve for the amplitudes of Gaussian kernels. Finally, a Bayesian framework is used on the Gaussian mixture model to assimilate observational data with model forecasts. This methodology effectively decouples a large uncertainty propagation problem into many small problems. A major advantage of the proposed approach is that it does not require the knowledge of system dynamics and the measurement model explicitly. The simulation results are presented to illustrate the effectiveness of the proposed ideas. Copyright © 2014 by Puneet Singla. Published by the American Institute of Aeronautics and Astronautics, Inc.

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