The error representation using the straight difference of two vectors in the inertial navigation system may not be reasonable as it does not take the direction difference into consideration. Therefore, we proposed to use the SE_2(3) matrix Lie group to represent the state of the inertial-integrated navigation system which consequently leads to the common frame error representation. With the new velocity and position error definition, we leverage the group affine dynamics with the autonomous error properties and derive the error state differential equation for the inertial-integrated navigation on the north-east-down local-level navigation frame and the earth-centered earth-fixed frame, respectively, the corresponding extending Kalman filter (EKF), terms as SE_2(3)-EKF has also been derived. It provides a new perspective on the geometric EKF with a more sophisticated formula for the inertial navigation system .
The error representation using the straight difference of two vectors in the inertial navigation system may not be reasonable as it does not take the direction difference into consideration. Therefore, we proposed to use the SE_2(3) matrix Lie group to represent the state of the inertial-integrated navigation system which consequently leads to the common frame error representation. With the new velocity and position error definition, we leverage the group affine dynamics with the autonomous error properties and derive the error state differential equation for the inertial-integrated navigation on the north-east-down local-level navigation frame and the earth-centered earth-fixed frame, respectively, the corresponding extending Kalman filter (EKF), terms as SE_2(3)-EKF has also been derived. It provides a new perspective on the geometric EKF with a more sophisticated formula for the inertial-integrated navigation system. Furthermore, we propose a SE_2(3)-based smoothing algorithm based on the SE_2(3)-based EKF .
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inertial navigation system
inertial-integrated navigation system. Furthermore, we propose a SE_2(3)-based smoothing algorithm based on the SE_2(3)-based EKF