Implementation of a Kinematic State Vector Perturbation Theory for Gravitational Recovery

Stemming from Newton's second law of motion, a perturbation theory aimed at geopotential recovery, based on purely kinematic state vectors, as originally proposed by (Xu, 2008), is implemented with refinements for a more practicable realization. The principal focus of the theory is to be able to deduce the gravitational field over arbitrary arc lengths, given continuous satellite orbital data derived from tracking with Global Navigation Systems of Satellites, such as GPS. As such, it (this approach) reduces the encumbrances that come with traditional methods based on dynamic modeling, as well as the kinematic short-arc procedure. Taking advantage of the linear relationship between the gravitational field and spherical harmonic coefficients, we demonstrate the feasibility to infer the geopotential field using one-day long arcs. This procedure is also adapted to the processing of low-low satellite-to-satellite tracking data, e.g., GRACE-like missions that offer extremely high precision in inter-satellite range and range-rate. The ability to model these data with the requisite commensurate precision is analyzed.