On the Numerical Implementation of a Perturbation Method for Satellite Gravity Mapping

Abstract

In 2008 P. Xu (Celest Mech Dyn Astron, 100:231–249) proposed a strictly kinematic perturbation method for determining the Earth’s gravitational field from continuous satellite tracking. The main idea is to process orbital arcs of arbitrary length, thus minimizing superfluous parameter estimation associated with stitching together short-arc solutions, and at the same time formulating the problem in terms of standard linear parameter estimation. While the original formulation appears mathematically robust, its nested quadruple along-track integrations are computationally challenging. We reduce the formulation to double integrals and show that the method is numerically not feasible as originally envisaged. On the other hand, by abandoning the rigorous Gauss-Markov formalism, we show the numerical feasibility of processing multiple-day orbital arcs. The methodology lends itself to high-low and low-low satellite-to-satellite tracking, or combinations thereof, as for GRACE-like systems.