Study on Boundaries of Eigenvalues in SVD Method for Autonomous Star Identification

The singular values are important invariant features in singular value decomposition (SVD) method for autonomous star identification. This paper theoretically analyzes the inherent relationship between the star vectors in field of view (FOV) and the eigenvalues of the Hermitian matrix formed by star vectors, which is performed as an equivalent study on singular values of the star vector matrix. Firstly, the SVD method for star identification is introduced briefly. Secondly, starting with the case of two star vectors, the boundaries of maximum, middle and minimum eigenvalues factorized by the Hermitian matrix is obtained and then the results with regard to n star vectors are derived in detail. In simulation, the statistical data verifies the presented results by selecting star vectors of random star tracker orientations in actual catalog. The conclusion of this study gives the explicit boundaries and provides useful guidance for matching eigenvalues in star identification process.