局域重力场球冠谐建模与联邦滤波相结合的重力匹配导航算法

doi:10.11947/j.AGCS.2023.20220609

摘要/Abstract

摘要： 本文提出一种基于联邦Kalman滤波器(federated Kalman filter,FKF)和局部重力场球冠谐分析(spherical cap harmonic analysis,SCHA)建模的水下重力匹配导航方法。首先基于适定边值问题构建FKF子系统滤波器的重力梯度复数组合观测量;然后采用改进球谐分析技术(adjusted spherical harmonic analysis,ASHA)优化局部重力场球冠谐建模方法,快速建立以匹配点为中心的局部海洋重力场与空间位置之间较为准确的移动窗口球冠谐模型,并依据该模型组建子滤波器量测方程;最后利用预测残差向量设计自适应信息分配因子将各子滤波器状态估值及协方差进行融合得到惯导位置误差最优估计量。试验结果表明:采用SCHA建模的重力FKF匹配算法24 h航行导航定位误差保持在1.1 n mile以内,导航定位精度提高85%以上;10 d长时间航行导航定位精度提高了88.7%。本文算法能够在一定程度上克服惯性导航系统由于时间推移误差积累的缺陷,提高系统导航定位精度,增加匹配算法的稳健性。

关键词: FKF, SCHA, 重力梯度, 复数组合, 匹配导航, ASHA

Abstract: An underwater gravity matching navigation method based on federal Kalman filter (FKF) and spherical cap harmonic analysis (SCHA) modeling of local gravity field is proposed. Firstly, based on the well posed boundary value problem, the gravity gradient complex combination observation of FKF subsystem filter is constructed. Then, adjusted spherical harmonic analysis (ASHA) is used to optimize the spherical crown harmonic modeling method of local gravity field, so as to quickly establish a more accurate moving window spherical crown harmonic model between the local ocean gravity field centered on the matching point and the spatial position. Based on this model, the measurement equation of sub-filter is established. Finally, the prediction residual vector is used to design an adaptive information distribution factor to fuse the state estimation and covariance of each sub-filter to obtain the optimal estimator of inertial navigation position error. The experimental results show that the gravity FKF matching algorithm modeled by SCHA keeps the positioning error of 24-hour navigation within 1.1 n miles, and the navigation positioning accuracy is improved by more than 85%; The positioning accuracy of 10 day long navigation has been improved by 88.7%. The algorithm can overcome the defect of the inertial navigation system due to the accumulation of time error to some extent, improve the navigation and positioning accuracy of the system, and increase the robustness of the matching algorithm.

Key words: FKF, SCHA, gravity gradient, complex combination, match navigation, ASHA

中图分类号:

P228

黄炎, 李姗姗, 李新星, 宋星光, 范雕, 万宏发. 局域重力场球冠谐建模与联邦滤波相结合的重力匹配导航算法[J]. 测绘学报, 2023, 52(11): 1844-1857.

HUANG Yan, LI Shanshan, LI Xinxing, SONG Xingguang, FAN Diao, WAN Hongfa. Underwater gravity FKF matching enhancement algorithm based on local SCHA modeling[J]. Acta Geodaetica et Cartographica Sinica, 2023, 52(11): 1844-1857.

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