Estimation of Relative Satellite Formation Element Positions in Near Circular Orbits
Abstract : Precise relative position determination of satellite formation elements in near circular orbits is the focus of this thesis. A Bayes filter is used for the estimator with the dynamics solution obtained by solving the time periodic, linearized system via Floquet theory. This approach is similar to that of the traditional Clohessy-Wiltshire treatment, however much more of the system's behavior is retained by using a linear, time periodic system. The dynamics model includes all zonal harmonics of the Earth as well as sectoral, tesseral, and air drag perturbations. The filter algorithm was fed three types of simulated measurements: relative Carrier-Phases Differential GPS data, Standard Positioning System GPS data and range measurements between each satellite. Simulations were conducted to investigate the accuracy obtainable with these measurements. Results obtained are on the order of the noise of the measurements, which is as low as 2 centimeters in each coordinate axis.