Global Positioning System (GPS) satellite orbits are modeled using Kolmogorov, Arnold, Moser (KAM) tori. Precise Global Positioning System satellite locations are analyzed using Fourier transforms to identify the three basis frequencies in an Earth Centered, Earth Fixed (ECEF) rotating reference frame. The three fundamental frequencies are 1) the anomalistic frequency, 2) a combination of earth's rotational frequency and the nodal regression rate, and 3) the apsidial regression rate. A KAM tori model fit to the satellite data could be used to predict future satellite locations. This model would allow rapid determination with fewer computational requirements than the typical method of integrating through an orbit.
Global Positioning System (GPS) satellite orbits are modeled using Kolmogorov, Arnold, Moser (KAM) tori. Precise Global Positioning System satellite locations are analyzed using Fourier transforms to identify the three basis frequencies in an Earth Centered, Earth Fixed (ECEF) rotating reference frame. The three fundamental frequencies are 1) the anomalistic frequency, 2) a combination of earth's rotational frequency and the nodal regression rate, and 3) the apsidial regression rate. A KAM tori model fit to the satellite data could be used to predict future satellite locations. This model would allow rapid determination with fewer computational requirements than the typical method of integrating through an orbit.
This research proposes the use of an existing signal of opportunity - namely x-ray pulsars - to improve the accuracy and robustness of the GPS satellite and clock estimation algorithm. Improvement in...
The Kolmogorov-Arnold-Moser (KAM) theorem states that lightly perturbed integrable Hamiltonian systems maintain their multiply periodic, toroidal motion in the phase space. The assertion that earth...
For over half a century, an increasing number of satellites have fragmented in orbit, creating a large amount of hazardous orbital debris which threaten the safety of useful functioning satellites...
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