Analytical Optimization on GNSS/Sonar Buoy Array Deployment for Underwater Positioning

Global navigation satellite system (GNSS)/acoustic positioning precision is comprehensively determined by both the configuration of GNSS buoys array and ranging precision. Thus, optimizing the GNSS buoys array is meaningful to improve the positioning accuracy and reliability. This paper proposes an analytical method for optimizing the GNSS buoys array with regard to the cutoff angle constraints for observations. By using the latest geometric dilution of precision (GDOP) minimization method developed by this paper and introducing a set of constrains considering the coplanar GNSS buoys and the cutoff angle limitation, we discuss the position dilution of precision (GDOP') minimization for underwater positioning circumstances and propose an algorithm for producing the configuration with the smallest GDOP. Moreover, we develop a method for searching the best configuration to achieve an isotropic positioning coverage within a given region by employing the concepts about the GDOP mean value and variance. In the experimental test, we take five GNSS buoys as an example to give full solutions based on the centralized GDOP' minimization as well as a unique solution for minimizing the GDOP' mean value. The effectiveness of the proposed method is verified by the simulation experiment. Our experiments show that within a region the centralized GDOP minimization may be equivalent to the GDOP' mean value minimization as well as the GDOP' variance minimization.