水下单信标导航算法研究及置信区间分析

Underwater single-beacon navigation algorithms and confidence interval analysis

为了优化单信标导航算法中导航点的选取以提高导航精度,本文分析并比较了不同水下单信标导航算法的置信区间。考虑了3种典型的水下单信标导航算法:基于时延信息的单信标导航算法、基于方位角信息的单信标导航算法以及联合使用时延和方位角信息的单信标导航算法。本文首先基于偏微分矩阵建立了3种方法的导航误差和各测量误差的关系式,在此基础上利用导航误差的协方差矩阵分析了时延测量误差和方位角测量误差对3种方法导航结果置信区间分布的影响。此外,本文从水平位置精度因子和置信椭圆这2个角度对3种方法导航结果的置信区间的分布进行了比较。理论推导及仿真表明:时延测量误差和方位角测量误差基于导航点和声信标的相对几何位置关系影响置信区间的分布,且基于时延的单信标导航算法的导航结果和基于方位角的单信标的导航算法的导航结果具有互补的特性。

To optimize the selection of navigation points in single-beacon navigation algorithms and improve navigation accuracy,the confidence intervals of different underwater single-beacon navigation algorithms are analyzed and compared in this study.Three typical underwater single-beacon navigation algorithms,namely,the time of arrival(TOA)-based method,the direction of arrival(DOA)-based method,and the TOA-DOA-based method,are considered.The relationships between the navigation and measurement errors of the three methods are established based on the partial differential matrix.On this basis,the influences of the TOA and DOA errors on the confidence interval distributions of the navigation results of the three methods are analyzed using the covariance matrix of navigation errors.In addition,the confidence interval distributions of the three navigation methods are compared from the perspectives of horizontal dilution of precision and confidence ellipse.The theoretical induction and simulation results suggest that the TOA and DOA errors affect the distribution of the confidence interval based on the relative geometrical relationship between navigation points and the beacon,and the navigation results of the TOA-and DOA-based methods are complementary.