Analytical Solution for Autonomous Determination of near Circular Orbits.

An analytical approach for satellite orbit determination methodology will be investigated in this work. The motivation for this study is the realisation that enhanced microsatellites can be expected which require accurate orbital knowledge and control onboard to support their payloads. However, a satellite tracking capability has not yet been implemented at Surrey even on the ground segment, as this would involve a considerable cost to maintain and operate. Advanced modern technology enables micro or nanosatellites to have low cost and low power Global Positioning System (GPS) receivers, which opens the way for onboard orbit determination. However, the heavy computational demand required for executing orbit determination has made such an approach unsuitable given the onboard processing environment. In order to overcome this problem, a novel analytical description of a perturbed orbit has been developed by focusing on near circular orbits which is appropriate for Low Earth Orbit (LEO) satellites. To use this analytic description of the orbit for orbit determination extensively reduces the computational demand as no numerical integrator is required to propagate the orbit, the variational equation of the orbit, or state transition matrix. Thus analytical solutions to the orbit perturbation problem are the main focus of this work. The majority of extensive studies made mainly in the late 50's to 60's on this subject considers the general case of orbits, so that the solutions are extremely lengthy and complex. Due to the conventional methods they have chosen, the solutions have a singularity when the eccentricity approaches zero and the argument of perigee becomes undefined. The new description of the perturbed motion of near circular orbits is developed in this work, which does not have a singularity when the eccentricity is zero. This novel description is a natural expansion of the epicyclic motion of a small eccentric orbit, which results in a much simpler expression in the solutions and provides a greater understanding of orbital geometry. A fully analytical orbit determination system is also developed based on this epicyclic description of a perturbed orbit. As this orbit estimator requires no numerical integration scheme, it has extensive computational advantages and suits most onboard applications. This analytical orbit estimator is practically implemented onboard UoSat-12, which is Surrey's 350 kg class minisatellite. It has been operated for more than two years, and has demonstrated reliable autonomous onboard orbit determination. The in-orbit orbit determination results as well as the evaluations of practical accuracy are also presented.