Geometrical aspects of differential GPS positioning

Differential GPS positioning is considered from the purely geometric point of view. The tetrahedron formed by two ground stations and two satellite locations is the basic geometrical building block for differential satellite positioning. Relationships between the various vectors involved in this tetrahedron are described. These relationships are used to develop linear mathematical models which relate the vector baseline between the two ground stations to various kinds of differential GPS observations. Geometrically, all proposed observation types can be considered as either differential range observations or differential range difference observations. In the absence of instrumental and refraction effects, it is found that differential range observations are geometrically superior to differential range difference observations. Some implications of these geometrical considerations to practical differential GPS positioning are discussed.