The Iteration Method For The Wahba Problem Solution

摘要

Wahba problem is the task of constrained optimization on SO(3). Solution of this task is vital for satellite attitude determination using star trackers. An iterative method having quadratic convergence is proposed. Each iteration of the proposed method is reduced to sequential rotation of the vectors and solving the system of linear algebraic equations. The method needs an initial approximation, which can be obtained by the TRIAD method. The quaternion form of the TRIAD method is given. One or two iterations are sufficient for finding the optimal solution using the proposed method. The primary advantage of the proposed method as compared with classical methods based on calculation of eigenvectors and singular decomposition is the simplicity of its implementation.