A closed-form formula to calculate geometric dilution of precision (GDOP) for multi-GNSS constellations

摘要

With the future global navigation satellite system (GNSS), the multi-GNSS constellations, which are composed of various single systems, will be the main navigation method in future. For the multi-GNSS constellations, the geometric dilution of precision (GDOP) is an important parameter used for satellite selection and the evaluation of positioning accuracy. However, the calculation of GDOP is a time-consuming and power-consuming task. Using Schur complement, we present a closed-form formula to calculate GDOP for multi-GNSS constellations. The formula can be applied to multi-GNSS constellations that include two, three or four different single systems. Furthermore, a closed-form formula for the case of exactly five satellites is also derived. Compared with the conventional numerical methods, the formula can reduce the amounts of multiplication and addition effectively. Numerical experiments validate the effectiveness and feasibility of the closed-form formula.