A mathematical model of pseudo-range single point positioning and its programming

In this paper, the mathematical model of pseudo-range single-point positioning is analyzed in detail, and detailed steps and error equations are listed, including coordinate transformation and some important technical details involved. The spatial rectangular coordinates XYZ of single-point positioning of each epoch of the station and coordinates calculated by synthesizing metadata of each epoch are calculated by programming. Using the original data obtained from some engineering surveys and converted into RINEX format, the coordinates of the surveying station are calculated by using the pseudo-range observation value of GPS satellite and navigation N file. The coordinates are compared and analyzed with the approximate coordinates calculated by the program of the receiver. The results show that the coordinates are about meter-level, while the accuracy of singlepoint positioning is meter-level. It is proved that the mathematical model is feasible and easy to be realized by programming.