A comparative analysis of star identification algorithms

Star Identification and Attitude Determination With Projective Cameras

“…we arrive atū i ∝ He i (10) It is observed, therefore, that the homography matrix H is only defined to an unknown scale-specifically, it is a 3 × 3 matrix having nine elements, but with only eight degrees of freedom. This interpretation of the star imaging problem (Fig.…”

“…It is also possible to choose a different number of stars and construct larger sets of independent invariants. For example, Toloei, et al, [10] construct a descriptor using combinations of inter-star angles and dihedral angles amongst a set of five stars. However, although three different five-star descriptors are presented in Ref.…”

“…However, although three different five-star descriptors are presented in Ref. [10], none of their proposed descriptors have the seven (10 − 3 = 7) independent invariants expected for a five-star asterism. This is noteworthy since five-star descriptors of less than seven invariants leave helpful information unused, while five-star descriptors of more than seven invariants include redundant information that does not enhance descriptiveness.…”

“…For a generic uncalibrated camera (either wide or narrow FOV), the projection of stars onto an image is governed by Eq. (10). That is, the transformation is described by the action of the projective general linear group, PGL 3, which has dimension 8.…”

“…Numerical simulations and live-sky experiments between different algorithms are important here, though simple changes to any choice in the pipeline can significantly effect overall performance-often making a fair comparison between competing algorithms difficult. Numerical comparisons of some existing algorithms may be found elsewhere [4], [5], [10]. The contribution of this manuscript is not the development of new star identification algorithms, but a better theoretical framework for understanding how the vast majority of these algorithms actually function.…”