New Three-Dimensional Assessment Model and Optimization of Acoustic Positioning System

This paper addresses the problem of assessing and optimizing the acoustic positioning system for underwater target localization with range measurement. We present a new three-dimensional assessment model to evaluate the optimal geometric beacon formation whether meets user requirements. For mathematical tractability, it is assumed that the measurements of the range between the target and beacons are corrupted with white Gaussian noise with variance, which is distance-dependent. Then, the relationship between DOP parameters and positioning accuracy can be derived by adopting dilution of precision (DOP) parameters in the assessment model. In addition, the optimal geometric beacon formation yielding the best performance can be achieved via minimizing the values of geometric dilution of precision (GDOP) in the case where the target position is known and fixed. Next, in order to ensure that the estimated positioning accuracy on the region of interest satisfies the precision required by the user, geometric positioning accuracy (GPA), horizontal 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 that only uses GDOP to optimize the formation and cannot assess the performance of the specified size, this new three-dimensional assessment model can evaluate the optimal geometric beacon formation for each dimension of any point in three-dimensional space, which can provide guidance to optimize the performance of each specified dimension.