Geometry of GPS dilution of precision: revisited

We revisit the geometric interpretation of GPS dilution of precision (DOP) factors giving emphasis on the geometric impact of the receiver clock parameter on the conventional GPS positioning solution. The comparison is made between the solutions with and without an estimated receiver clock parameter, i.e., conventional GPS versus pure trilateration solution. The generalized form of the DOP factors is also presented for observation redundancy greater than zero. The DOP factor equations are established as functions of triangle surfaces and tetrahedron volumes formed by the receiver-satellite unit vectors or by these vectors between themselves. To facilitate the comparison of the solutions with and without a receiver clock parameter, the average of receiver-satellite unit vectors is introduced to interpret the DOP factors geometrically. The geometry of satellite outage is also revisited from a geometric point of view. Finally, the geometric interpretation of receiver clock constrains within a positioning solution is also investigated.