Formation design and relative navigation in high Earth orbits

This dissertation focuses on three key elements of precision satellite formation flying: formation design; relative navigation; and sensor and measurement modeling. Formation flying in high Earth orbit (HEO) is complicated by the difficulty of accurately modeling relative dynamics in highly eccentric orbits and the sparse nature of tracking data at high altitudes. This research develops a formation design tool and extended Kalman filter that mitigate these factors by representing the relative motion in Keplerian element space rather than conventional rectangular position and velocity coordinates and presents the measurement models and preliminary data generation techniques necessary for processing reflected GPS and reflected crosslink observations in a relative navigation filter.; Geometrical methods for formation design based on simple relative motion models originally intended for rendezvous in low Earth orbit (LEO) have been previously developed and used to specify desired relative motions in near circular orbits. A comparable set of geometrical relationships for formations in eccentric orbits are developed here. This approach offers valuable insight into the relative motion and allows for the rapid design of satellite configurations to achieve mission specific requirements, such as vehicle separation at perigee or apogee, minimum separations, or a particular geometric shape. The expressions formulate the relative motion in terms of a constant set of Keplerian element differences and are valid for arbitrary eccentricities. The use of these relationships to investigate formation designs and their evolution in time is demonstrated. In addition, the long-term effects of unmodeled perturbations on the desired formation geometry are shown in several examples.; Formation flying in HEO relies on accurate relative navigation information for precise formation control and accurate interpretation of science data. An extended Kalman filter for relative navigation in HEO is developed that enhances the linearity of the dynamic model by framing the state in Keplerian elements. The filter design includes the ability to process reflected GPS and reflected satellite-to-satellite crosslink measurements. The performance of the filter is presented for a set of formation flying scenarios in medium-to-high Earth orbits with limited visibility of the GPS constellation. The effect of higher order gravity terms, solar radiation pressure, third-body effects of the Sun and Moon, and atmospheric drag on estimation accuracy is considered. Relative semimajor axis accuracy of 0.070 m and relative position and velocity accuracy of 0.93 m and 0.070 mm/s, respectively, are obtained for vehicles separated by 10--170 km using GPS measurements only. This represents an order of magnitude improvement over previously reported relative navigation performance in HEO.