Coarse Alignment Method Using Manifold Optimization for Sins on a Rocking Base

This paper proposes a coarse alignment method using manifold optimization to solve the initial alignment problem of the strapdown inertial navigation system (SINS) on a rocking base. In this method, the initial coarse alignment of SINS is transformed from the constrained optimization problem in Euclidean space to an unconstrained optimization problem in Manifold space. There are two innovations in this method: the first is the optimization method of gradient descent in Euclidean space, which is reviewed and extended to manifold space. By combining the trust region method with the Barzilai-Borwein method, the optimal selection of the iterative update step on the tangent space of the manifold is realized, which ensures the efficient and stable convergence of the algorithm. Secondly, the Cayley transform is used to construct the retraction mapping, and its closed form analytic solution and structure preservation characteristics are used to effectively suppress the error accumulation caused by numerical approximation, to ensure that the iterative points on the tangent space of the manifold are mapped to the manifold space. The experiment results indicate that the proposed coarse alignment method performs better than the existing methods.