A Geometric-Nonlinear Optimization Algorithm for Solving Pose Matrices in Aircraft Visual Navigation

We propose a noniterative geometric dimensionality reduction algorithm for solving the pose estimation problem of an onboard camera in visual navigation. Considering the characteristic of long imaging distances in aerial vehicle navigation and under the assumption of a planar distribution of feature points, we simplify the pose estimation problem to one that involves estimating the rotation matrix using a homography matrix, and we introduce the corresponding geometric dimensionality reduction algorithm. To ensure the robustness of the algorithm under extreme conditions, we reformulate the problem of solving for the rotation matrix as a nonconvex optimization problem and propose a nonlinear optimization algorithm as a fallback strategy when the geometric dimensionality reduction algorithm fails. Extensive numerical experiments demonstrate that the proposed hybrid geometric-nonlinear optimization approach exhibits strong stability and efficient numerical performance.