Analytical optimization on GNSS buoy array for underwater positioning

Global navigation satellite system (GNSS)/acoustic positioning precision is determined by the positioning geometry and the ranging precision; thus optimizing GNSS buoys array is meaningful to improve the positioning accuracy and reliability. An analytical method is proposed for optimizing the GNSS buoys array with regard to the cutoff angle constraints for underwater acoustic observations. For the practical limitation of coplanarity of GNSS buoys and the cutoff angle, an algorithm is proposed to analytically minimize the position dilution of precision (PDOP). The proposed method is validated to give complete solutions of PDOP minimization with five GNSS buoys. At last, in order to search a best configuration among the PDOP solution set, we propose a search algorithm to get the solution with the smallest geometric dilution of precision (GDOP). It indicates that within a given region, the GDOP minimization at the center of a region is equivalent to the PDOP mean minimization over the region. The relation between the positioning accuracy and the positioning geometry with five known points is illustrated in an experiment performed in South China Sea.