Before revision:  The INS/GPS and INS/Odometer integration are investigated as two representatives of inertial based applications . Some application aspects of the derived error state models in the two applications are presented, which include how to select the error state model, initialization of the SE2(3) based error state covariance and feedback correction corresponding to the error state definitions.
After revision:  The INS/GPS and INS/Odometer integration are investigated as two representatives of inertial based integration . Some application aspects of the derived error state models in the two applications are presented, which include how to select the error state model, initialization of the SE2(3) based error state covariance and feedback correction corresponding to the error state definitions.