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Tracking GPS orbits using KAM theory

This paper discusses attempts to model GPS orbits as KAM tori. KAM tori are formed when weak perturbations on a Hamiltonian system result in perturbed tori structures, in the absence of resonance. These tori are topologically equivalent to “donut” shapes in phase space. Solutions to the unperturbed system persist, but are slightly changed in these tori structures. The potential to model GPS orbits using KAM theory exists, however trajectory following methods need to be modified from their current form. Two numerical algorithms for constructing a KAM torus are explored, and an approach of applying trajectory following methods is investigated. Application of the KAM theorem on GPS operations has huge upside-potential because it would decrease computational burdens. If orbital tori prove to be sufficiently accurate, the validity of the ephemerides will have a much longer useful life. Since the ephemerides of current methods are only useful for several hours, orbital tori need only provide days of stability to decrease operational burdens. This may have the most significant impact on GPS operations in history.