This paper addresses the problem of assessing and optimizing acoustic positioning system for underwater target localization with range measurements only. We present a new three-dimensional assessment model to assess the optimal geometric beacon formation whether meet user needs. For the sake of mathematical tractability, it is assumed that the measurements of the range between the target and beacons are corrupted with white Gaussian noise with variance is distance-dependent. Then by adopting dilution of precision (DOP) parameters in the assessment model, the relationship between DOP parameters and positioning accuracy is derived. In addition, the optimal geometric beacon formation that will yield the best performance is achieved by minimizing the values of geometric dilution of precision (GDOP) on condition that the position of target is known and fixed. Next, in order to make sure whether the estimate positioning accuracy over interesting region satisfy the precision needed by the users, geometric positioning accuracy (GPA), horizonal positioning accuracy (HPA) and vertical positioning accuracy (VPA) are utilized to assess the optimal geometric beacon formation. Simulation examples are designed to illustrate the exactness of the conclusion. Unlike other work which only use GDOP to optimize the formation and cannot assess the performance of the specified dimensions, this new three-dimensional assessment model can assess the optimal geometric beacon formation in each dimension for any point in three-dimensional space, which can provide users with guidance advices to optimize performance of every specified dimension.