This paper presents a three-dimensional (3D) spatial localization algorithm by using multiple one-dimensional uniform linear arrays (ULA). We first discuss geometric features of the angle-of-arrival (AOA) measurements of the array and present the corresponding principle of spatial cone angle intersection positioning with an angular measurement model. Then, we propose a new positioning method with an analytic study on the geometric dilution of precision (GDOP) of target location in different cases. The results of simulation show that the estimation accuracy of this method can attain the Cramér-Rao Bound (CRB) under low measurement noise.