SINS/DVL Linear Initial Alignment Based on Lie Group SE3(3)

This article investigates the strapdown inertial navigation system's (SINS's) initial alignment, aided by the Doppler velocity log (DVL). A linear Kalman filtering method is proposed using the theory of the Lie group, which is immune to initial misalignment. The dead-reckoning position based on the body velocity provided by DVL and attitude provided by SINS is used as measurement. The SINS-calculated attitude, velocity, position, and DVL dead-reckoning position are formulated together as the elements of Lie group $S{E}_3(3)$. Since the dead-reckoning position is a type of left-invariant measurement, the corresponding linear error-state model is derived based on the left-invariant group error definition. Although the Lie group state model is not group affine, the small-attitude-error assumption does not introduce accuracy degeneracy in deriving the linear error-state model. This is the core reason why the derived linear error-state model is still applicable for cases with large initial misalignments. Experiments are conducted to verify the feasibility and effectiveness of the proposed method. The test results show that the proposed method has higher accuracy and faster convergence speed compared with the existing methods.