Analysis of GDOP in the Passive-ranging Location System Design

Geometric dilution of precision (GDOP) is one of the most important factors for judging whether a positioning system is of high-accuracy. An analysis model of GDOP is constructed, which can help to analyze the variations of GDOP going with the changes of geometrical position in the three-dimensional space. With the analysis of both calculation arithmetic of GDOP and typical 3-dimensional passive-ranging positioning system of 4-stations, we get that positioning accuracy, of which the ranging accuracy is the root, will obviously fluctuate and regularly change following the variations of user’s position. Using a sphere as the geometrical reference, GDOP will fluctuate variously or be almost constant at different “longitudes” and “latitudes”, increase along a radial, and be discontinuous near a base station. These results could provide useful information for the users to select the stations and work area, which also can give the designers of passive-ranging positioning system some advices about deploying stations. Firstly, for the purposes of maintaining a proper positioning accuracy, safe distance should be suggested around the stations. Besides, the users should stay in the reference geometry, if possible. At last, in the beginning of a design, the factors, such as the limit of users’ location region, should be taken into account.