Robustness analysis and improvement of singular value decomposition algorithm for autonomous star identification

Abstract

This paper presents a comprehensive robustness analysis of singular value decomposition (SVD) algorithm for autonomous star identification and proposes an improved method based on the analytical results. Firstly, the SVD algorithm-based star identification is introduced and the inherent relationship between the eigenvalue and eigenvector and observed stars is expounded theoretically. Secondly, the error models of SVD algorithm in terms of position error, magnitude error, and mistaken stars are derived and formulated respectively, and then their robustness are investigated according to the different eigenvalues and eigenvectors of the characteristic matrix. Thirdly, a novel star-selection method is proposed to enhance the ability to tolerate errors by adopting three strategies: reduced pattern star number, pivot star constraint, and cost function criterion. In addition, a convenient and reliable validation process is designed by using inner product of matched star vectors. Finally, a number of experiments are carried out by statistics of 10,000 random star tracker orientations. The simulation results show that the improved SVD algorithm provides better performance, whose identification rate reaches up to 99.08% without errors. Besides, it makes the existing SVD algorithm more robust by increasing the original identification rate to about 90% or higher when errors exist.