基于高斯勒让德-二分迭代的实际导航性能评估方法  

Actual navigation performance evaluation method based on Gauss-Legendre-bisection iteration

作　　者：钟伦珑[1] 袁旭 董巧丽[2] 王崇赓 ZHONG Lunlong;YUAN Xu;DONG Qiaoli;WANG Chonggeng(Tianjin Key Laboratory for Advanced Signal Processing,Civil Aviation University of China,Tianjin 300300,China;College of Science,Civil Aviation University of China,Tianjin 300300,China)

机构地区：[1]中国民航大学智能信号与图像处理天津市重点实验室,天津300300 [2]中国民航大学理学院,天津300300

出　　处：《中国惯性技术学报》2025年第2期196-204,212,共10页Journal of Chinese Inertial Technology

基　　金：国家重点研发计划项目(2020YFB0505603)。

摘　　要：针对传统实际导航性能(ANP)迭代评估方法准确性和快速性难以均衡的问题,提出了一种基于高斯勒让德-二分迭代的ANP评估方法。首先,建立了ANP评估的数学模型,基于多传感器融合滤波理论,在位置估计协方差矩阵的特征值基础上,建立位置估计误差的二维概率密度函数,将组合导航的ANP评估建模成置信域表征参数求解问题。然后,应用高斯勒让德数值积分法减小每次迭代的运算量,同时结合二分迭代快速收缩搜索区间,减小方法迭代次数,避免动态积分区间带来的求积节点数选取困难问题,在保障准确性的同时提高快速性。仿真结果表明,与基于复化Simpson公式的传统方法相比,所提方法可在相同准确性要求下,将平均计算时间由15.69 ms减少到1.09 ms。Aiming at the difficulty of balancing the accuracy and speed of traditional iterative evaluation methods for actual navigation performance(ANP),an ANP evaluation method based on Gauss-Legendre-bisection iteration is proposed.Firstly,a mathematical model for ANP evaluation is established.Based on multi-sensor fusion filtering theory,a two-dimensional probability density function of the position estimation error is established on the basis of the eigenvalue of the position estimation covariance matrix,and ANP evaluation of integrated navigation is modeled as a solving problem of confidence region representation parameter.Then,Gauss-Legendre numerical integration method is applied to reduce the amount of calculations at each iteration.Meanwhile,bisection iteration is integrated to quickly shrink the search interval,thus reduce the number of iterations,as well as avoid the problem of difficult selection of the number of quadrature nodes caused by the dynamic integral interval,and improve the rapidity while ensuring the accuracy.Simulation results show that compared with the traditional method based on complex Simpson formula,the proposed method can reduce the average computing time from 15.69 ms to 1.09 ms under the same accuracy requirements.

关 键 词：多传感器融合 组合导航 实际导航性能 高斯勒让德 二分迭代 

分 类 号：U666.1[交通运输工程—船舶及航道工程]