Stellar Instrument Magnitude Estimation in Infinite-Dimensional Space

摘要

The guide star catalog generation is based on the estimation of stellar instrument magnitudes and the performance and the reliability of star identification algorithms can also be improved by this estimation. This task is critical for the design of advanced star sensors. In this study, a novel method for estimating stellar instrument magnitudes is presented. In this method, the functions of the star illuminance and spectral responsivity of detectors are considered infinite-dimensional vectors in Hilbert space, where the model between star illuminance and magnitudes in each band is established. All feasible solutions for star illuminance that meet the corresponding magnitudes in a band are considered curves in infinite-dimensional space. Accordingly, the solution for star illuminance as the intersection of curves originating from magnitudes in multiple bands can be calculated by solving the corresponding redundant equations. Then, stellar instrument magnitudes can be obtained. An optimization algorithm with limited step lengths and directions that can accurately and quickly solve the problem is proposed and applied to effectively solve the aforementioned equations. An error model is also established in infinite-dimensional space to minimize estimation error, and an optimal band selection rule used in the redundant equations is provided. A simulation experiment is conducted, and its RMSE is 11% lower than the best existing approach. In addition, the night sky experiment performed in this study demonstrates that the proposed method cannot only guarantee accuracy but can also adapt to a wide spectral range.