Currently, there is an increasing demand for positioning and tracking objects, personnel and vehicles for civil and military applications. Most wireless positioning methods can be classified as wideband systems as the positioning accuracy largely depends on the available bandwidth and they require a wide bandwidth to achieve a high accuracy measurement of the time difference of arrival (TDoA) (K. Yu, I. Sharp and Y. J. Guo, Ground-Based Wireless Positioning, IEEE Digital and Mobile Communications Series, John Wiley and Sons Ltd., 2009). CSIRO has developed a wideband positioning system called WASP. In WASP trials, it is found that it can be very difficult to have access to a large chunk of unused spectrum. Moreover, in order to obtain positional information in the vertical direction using TDoA based methods, one needs to place a number of sensors vertically, which can be difficult in many deployment scenarios. This motivated us to conduct research on three dimensional (3D) positioning using uniform circular arrays (UCA). Since a uniform circular array can provide the elevation and azimuth information of the signal bearing by using DoA estimation techniques, one can achieve high accuracy 3D positioning by deploying a number of uniform circular arrays in a horizontal plane. Although UCAs have been employed in direction finding applications, there have been very limited reports on their applications in positioning and tracking involving multiple arrays. In this paper, we present a systematic study on three dimensional wireless positioning using uniform circular arrays. The contributions of the paper include the following: a) The theoretical framework of a three dimensional positioning method employing multiple uniform circular arrays; b) The derivation of the optimum weighting function required by the weighted least squares method to improve the positioning accuracy; and c) A performance assessment of the proposed positioning method.