GDOP minimum in multi-GNSS positioning

In positioning, navigation and timing (PNT) applications with the Global Navigation Satellite System (GNSS), the geometric dilution of precision (GDOP) offers an important index for selecting satellites from all tracked satellites for positioning calculation. In general, the lower the GDOP values are, the more accurate the PNT solution is. Therefore, the GDOP minimum should be pursued. In this paper, we mainly focused on the GDOP minimum when the single-point positioning is based on the integration of three GNSSs. The GDOP minimum for any number of tracked satellites is theoretically derived in this paper. In addition, when the number of the satellites is equal to that of the unknown parameters, the correctness of GDOP minimum obtained has also been validated from two different perspectives.