Abstract
This paper investigates the impact of navigation errors on the navigation and control aspects of formation flying spacecraft. The use of carrier-phase differential Global Positioning System measurements in relative navigation filters is analyzed, with a particular focus on the semimajor axis error. Semimajor axis error is shown to be the sum of two positive quantities that are related to the satisfaction of the balance and correlation requirements. Previous publications have suggested that a good navigation filter would yield estimates of the along-track velocity and radial position that are strongly correlated. However, practical experience with filters based on the carrier-phase differential Global Positioning System measurements has shown that this seldom occurs, even when the estimation accuracies are very good. Analytical methods and numerical simulations are used to show that the optimal semimajor axis estimate from a Kalman filter does not satisfy these requirements for any combination of measurement and process noise. Numerical examples with a fully nonlinear extended Kalman filter appear to bear out these conclusions. The combination of these simulations and analysis provides new insights on the crucial role of the process noise in determining semimajor axis knowledge.
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