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The positioning performance of ultra-wideband (UWB) system based on time difference of arrival (TDOA) depends on two factors including ranging accuracy and location of base stations. In this paper, the average geometric dilution of precision (GDOP) is analyzed when the layout of base stations is near optimal for the positioning based on TDOA. The closed expression for the number of base stations and the average GDOP is given by least square fitting. Additionally, the signal attenuation caused by the varying distribution radius of the base stations is taken into account, while Cramer Rao lower bound (CRLB) is introduced as the indicator for performance to create the function for the optimal distribution radius of base stations and the radius of the area. These results can provide an effective reference for optimizing the positioning accuracy and energy efficiency of a UWB system.

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