Geometry optimization for GPS navigation

This paper presents the analysis and numerical optimization of the geometry of an inverted pseudolite positioning system. First, the effect of geometry on the system's accuracy is examined. The geometric dilution of precision produced by typical system geometry is considered, and an alternate measure of the geometry effect, the condition number of the "visibility" matrix H, is introduced. Next, the optimization of the system's geometry is presented. The simplified problem of optimizing the geometry with respect to a stationary pseudolite is solved. The results of a numerical optimization are presented and both the effectiveness of the optimization routine and the usefulness of the resulting system configurations are discussed. Finally, design guidelines for good geometry are listed.