Supplementary correction algorithm for integrated navigation under insufficient initial alignment

• Propose a real-time backtracking framework based on the state augmentation and geometric decomposition of EKF, eliminating traditional data storage and repeated filtering • Develop a supplementary correction algorithm based on real-time backtracking and the STEKF algorithm, which removes navigation errors from the initial misalignment angle • The SINS/DVL integration experiment results show that under insufficient alignment conditions, the supplementary correction algorithm achieves positioning accuracy close to that of integrated navigation under good alignment conditions Insufficient initial alignment in some integrated navigation systems can induce more rapid error accumulation in the subsequent navigation process. To address this issue, this paper proposes a supplementary correction algorithm framework based on real-time backtracking. First, the initial state is expanded into the state vector of the extended Kalman filter (EKF). Through geometric expansion of the EKF, the weight of the initial state value in the current state estimate is quantitatively determined, enabling real-time updates to the current state estimate. This approach approximates restarting the filtering with the corrected initial value, eliminating the need for data storage and repeated filtering processes required by traditional backtracking algorithms. Based on the real-time backtracking method and the state transformation extended Kalman filter (STEKF), a general supplementary correction algorithm framework for integrated navigation is constructed, capable of isolating and eliminating navigation errors introduced by the initial alignment error. Experimental results from SINS/DVL integrated navigation demonstrate that when the initial attitude contains certain errors, the proposed supplementary correction algorithm can effectively reduce navigation errors, achieving accuracy levels close to those with well initial alignment.