Minimum of Geometric Dilution of Precision (GDOP) for five satellites with dual-GNSS constellations

The Geometric Dilution of Precision (GDOP) is a term to specify multiplicative effect of the satellite geometry on positioning and timing precision. For positioning, navigation and timing (PNT) applications with multi-GNSS constellations, the lower the GDOP values are, the more accurate the PNT solution is, and thus, the minimum value of GDOP should be discussed. Firstly, this paper analyses the traditional method for calculating the minimum of GDOP for dual-GNSS constellations. Then, from the point of the practical constraints of a GNSS receiver on the earth surface, a new formula for the specific minimum of GDOP together with the design matrix is derived. The minimum of GDOP is expressed as a function with two satellite elevation angles as variables. The numerical experiments have demonstrated the validation of the new formula for the minimum of GDOP.