一种世界坐标系下的GNSS/SINS松组合导航矩阵李群滤波算法  

Matrix Lie group filtering algorithm for GNSS/SINS loosely integrated navigation in the world frame

作　　者：郭迟[1,2,3] 陈毅超 罗亚荣 GUO Chi;CHEN Yichao;LUO Yarong(GNSS Research Center,Wuhan University,Wuhan 430079,China;Hubei Luojia Laboratory,Wuhan 430079,China;Institute of Artificial Intelligence,Wuhan University,Wuhan 430079,China)

机构地区：[1]武汉大学卫星导航定位技术研究中心,武汉430079 [2]湖北珞珈实验室,武汉430079 [3]武汉大学人工智能研究院,武汉430079

出　　处：《中国惯性技术学报》2024年第3期242-249,共8页Journal of Chinese Inertial Technology

基　　金：博士后科学基金项目(2023TQ0248);湖北珞珈实验室开放基金(230100007);湖北省重大科技专项(2022AAA009)。

摘　　要：针对在地心地固(ECEF)坐标系下基于右不变误差的卡尔曼滤波在GNSS/SINS组合导航中,因位置矢量数值较大导致系统线性误差运动学矩阵和观测矩阵不稳定进而降低滤波器性能的问题,提出一种世界坐标系下的GNSS/SINS松组合导航矩阵李群滤波算法。首先在世界坐标系中构建导航状态和考虑地球自转的运动学方程。然后在世界坐标系下定义矩阵李群上的右不变误差,该误差在右群作用下保持不变,并重新推导和设计基于该误差的矩阵李群滤波算法,根据GNSS观测构建世界坐标系下的观测矩阵。实验结果表明,在低精度惯导场景中相对于ECEF坐标系下的传统扩展卡尔曼滤波,所提算法的北向、东向、地向位置误差均方根分别减小了82.6%、61.8%和10.6%,具有一定的实用价值。In the GNSS/SINS integrated navigation,the Kalman filter based on right invariant error constructed in the earth-centered earth-fixed(ECEF)frame is unstable in the linear error dynamics matrix and observation matrix due to the large value of the position vector,leading to a decrease in filter performance,so a matrix Lie group filtering algorithm for GNSS/SINS loosely integrated navigation in the world frame is proposed.Firstly,the navigation state and the kinematic equation considering the rotation of the Earth are constructed in the world frame.Then the right invariant error on the matrix Lie group is defined in the world frame,and the error remains unchanged under the action of the right group.The matrix Lie group filtering algorithm based on the error is re-derived and designed,and the observation matrix in the world frame is constructed according to GNSS observations.Experimental results show that compared with the traditional extended Kalman filtering in the ECEF frame,the root mean square of the position error of the proposed algorithm in the north,east and down direction are reduced by 82.6%,61.8%,and 10.6%respectively in the consumer grade IMU scenario,which has certain practical value.

关 键 词：组合导航 矩阵李群 卡尔曼滤波 世界坐标系 

分 类 号：U666.1[交通运输工程—船舶及航道工程]