The Optimized SINS/DVL Integration Based on SE₃(3) Quaternion Error Model and Adaptive Estimator

In this article, the strapdown inertial navigation system/Doppler velocity log (SINS/DVL) is improved from the perspectives of mathematical model and data fusion algorithm. The optimized SINS/DVL integration based on Lie group SE3(3) quaternion error model and adaptive estimator is investigated. For mathematical model, the SE3(3) quaternion error model for SINS/DVL is proposed to replace traditional model. First, the attitude state is represented by quaternion, and the SINS mechanization satisfying group affine property based on quaternion is constructed. Second, the dead-reckoning (DR) of DVL and the attitude, velocity, and position of SINS are defined as elements of SE3(3). Then, the quaternion error state space model, measurement model, and feedback correction based on SE3(3) are derived. The proposed model extends the application of Lie group in quaternion error model. For data fusion algorithm, in response to the issues of unknown measurement noise of DR, combining with the linear property of the SE3(3) measurement model, the quaternion estimator based on variational Bayesian (VB) and edge sampling (ES) is proposed. Finally, the performance of the investigated SINS/DVL integration is evaluated through two field tests. The results show that the proposed integration has better convergence velocity and accuracy than existing methods.