The Mathematical Expectation of GDOP and its Application

Abstract

Along with the development of Global Navigation Satellite System (GNSS) and the deepening of research on Interoperability, more navigation satellites in space are able to provide Position Velocity and Time (PVT) service for users. Although added visible satellite number leads a better Geometric Dilution of Precision (GDOP), there is not a conclusion about this GDOP improvement in quality. In this paper, we obtain another expression of GDOP using two variables, azimuth and elevation, instead of the used three direction cosines. Then, suppose the two variables as random variable, we obtain the expression of the mathematical expectation of GDOP, which means the average GDOP when the satellites randomly appear in the visible space. After that, considering the different block situation of user, the minimal elevation angle is imported as a constraint condition, and we obtain the expression of GDOP mathematical expectation with the minimal elevation angle limitation. Furthermore, a simulation process is adopted to verify the foregoing expressions. At last, an assessment model of GNSS constellation using the GDOP mathematical expectation is constructed and which is employed to evaluate the constellation of interoperability between different GNSSs.