Analytical evaluation of geometric dilution of precision for three-dimensional angle-of-arrival target localization in wireless sensor networks

Abstract

This article focuses on the evaluation of geometric dilution of precision for three-dimensional angle-of-arrival target localization in wireless sensor networks. We calculate a general analytical expression for the geometric dilution of precision for three-dimensional angle-of-arrival target localization. Unlike the existing works in the literature, in this article, no assumptions are made regarding the observation ranges, noise variances, or the number of sensors in the derivation of the geometric dilution of precision. Necessary and sufficient conditions regarding the existence of geometric dilution of precision are also derived, which can be readily used to evaluate the observability of three-dimensional angle-of-arrival target localization in wireless sensor networks. Moreover, a concise procedure is also presented to calculate the geometric dilution of precision when it exists. Finally, several examples are used to illustrate our results, and it is shown that the performance of the proposed regular deployment configurations of angle-of-arrival sensors is better than the one with random deployment patterns.