Initial alignment plays a pivotal role in inertial navigation systems, as even small orientation errors introduced at startup can significantly degrade subsequent positioning and attitude estimates. In this context, we propose a novel inverse alignment method for rotational inertial navigation that leverages the group affine property and high-speed computing to accelerate and refine the alignment process. Adopting inverse navigation and Lie group theory, we derive a left-invariant error model in the geocentric geosynchronous coordinate framework and rapidly achieve alignment by integrating forward and inverse Kalman filtering. During 2.5-h in-vehicle tests, our approach reduced both the maximum error and CEP (Circular Error Probable 50%) by 60% compared to standard alignment methods, and it surpassed the performance of conventional group affine alignment by improving accuracy by 7.2% and 20%, respectively. These results highlight the method’s ability to deliver swift, precise alignment across diverse initial misalignment angles, offering significant benefits for modern high-precision inertial navigation applications.
