In order to improve the real-time performance and solution accuracy of star sensor, based on multi-vector information, a quaternion representation method for solving three-axis rotation angle of star sensor was proposed, and the method was derived in detail theoretically. Based on the three-dimensional coordinates of a single starlight vector in celestial coordinate system and star sensor coordinate system, the direction cosine matrix transformation form was transformed into quaternion transformation form. The quadratic quaternion transformation form was reduced in order to facilitate the subsequent solution. Considering the weight of different starlight vectors, the information of all starlight vectors was combined to solve the three-axis rotation angle of the star sensor. A specific solution was given, aiming at the iteration uncertainty and the direction singularity of quaternion vector in the process of solving three-axis rotation angle, The performance of the proposed algorithm was compared with that of the traditional algorithm. Simulation results show that the proposed algorithm has faster solving speed and higher accuracy in solving three-axis rotation angle than the traditional algorithm.
Fig.1Schematic diagram of starlight vector imaging
Fig.2Three-axis attitude angle error curve of different algorithms under 1.0×10−3 standard deviation of noise
算法
σA/(°)
σs=1.0×10?2
σs=1.0×10?3
σs=1.0×10?4
σs=1.0×10?5
SVD
2.071×10?1
2.751×10?2
3.084×10?3
4.055×10?4
LS
3.679×10?1
3.794×10?2
4.286×10?3
4.622×10?4
QUEST
2.071×10?1
2.751×10?2
3.084×10?3
4.055×10?4
本研究
2.071×10?1
2.751×10?2
3.084×10?3
4.055×10?4
Tab.1Standard deviation of attitude angle error for different algorithms with different noise standard deviations
Fig.3Time consumption curve of different algorithms under 1.0×10−3 standard deviation of noise
算法
t/s
σs=1×10?2
σs=1×10?3
σs=1×10?4
σs=1×10?5
SVD
6.021×10?5
5.971×10?5
6.153×10?5
6.568×10?5
LS
9.354×10?5
9.219×10?5
9.612×10?5
9.674×10?5
QUEST
5.721×10?5
5.671×10?5
5.953×10?5
5.368×10?5
本研究
3.284×10?5
3.322×10?5
3.268×10?5
3.109×10?5
Tab.2Time-consuming table for different algorithms with different noise standard deviations
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