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Geometric dilution of precision (GDOP) has been widely used as an accuracy metric for navigation and tracking systems. Since high accuracy in a positioning system requires both accurate measurement of the range and a good geometric relationship between the mobile device and the measuring points, the analysis of GDOP is an essential feature in determining the performance of a positioning system. In this paper, we perform GDOP analysis to obtain concise analytical expressions for a number of scenarios, which are generally applicable to geometries where the mobile device is surrounded by base stations. Comparison of the analytical results with simulations using the typical geometries of indoor positioning systems shows good agreement, except when the mobile position is close to a base station. This effect is a consequence of the ranging errors being a significant proportion of the range in short-range tracking systems and discontinuities in GDOP at the base station. The results provide useful information for the design and testing of tracking systems, as well as for the determination of the geometric deployment of base stations for good GDOP in the coverage area.