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.
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