引用本文: 齐珂, 曲国庆, 苏晓庆, 薛树强, 刘以旭, 杨文龙. 水下声纳定位浮标阵列解析优化[J]. 武汉大学学报 ( 信息科学版), 2019, 44(9): 1312-1319.
QI Ke, QU Guoqing, SU Xiaoqing, XUE Shuqiang, LIU Yixu, YANG Wenlong. Analytical Optimization on GNSS/Sonar Buoy Array Deployment for Underwater Positioning[J]. Geomatics and Information Science of Wuhan University, 2019, 44(9): 1312-1319.
 Citation: QI Ke, QU Guoqing, SU Xiaoqing, XUE Shuqiang, LIU Yixu, YANG Wenlong. Analytical Optimization on GNSS/Sonar Buoy Array Deployment for Underwater Positioning[J]. Geomatics and Information Science of Wuhan University, 2019, 44(9): 1312-1319.

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

• 摘要: 全球导航卫星系统（global navigation satellite system，GNSS）/声纳水下定位精度主要取决于GNSS浮标阵列构型和声学测距精度。优化水面浮标阵列是提高水下定位精度的重要途径。探讨了GNSS浮标阵列解析优化方法，算例以5枚和6枚浮标布设为例，应用所提方法给出了最优浮标阵列解。基于几何精度因子（geometric dilution of precision，GDOP）最小构型解析方法，通过考虑水下定位GNSS浮标位于水面和存在高度角限制这一约束条件，对水下定位浮标阵列进行了解析优化。由于浮标进行水下定位时是范围性的，还基于区域GDOP均值和方差两个指标对GNSS浮标阵优化问题进行了探讨，并采用数值方法设计了区域GDOP均值最小构型搜索算法。研究表明，虽然存在高度角约束条件，最优浮标阵列几何结构并不唯一，若在此基础上进一步考虑区域GDOP均值和方差最小的目标，则最终可获得唯一的区域均值浮标阵列结构。

Abstract: 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.

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