考虑传统的星敏感器标定方法忽略了星敏感器的畸变与光学参数之间的相互作用而引入的额外误差, 提出了一种基于非线性优化的星敏感器自主标定算法。该算法首先忽略星敏感器畸变的影响, 构建目标函数, 利用Levenberg-Marquardt非线性优化算法优化星敏感器的光学参数; 然后, 将得到的光学参数估计值作为理想值, 通过线性最小二乘法估计相机的镜头畸变系数; 最后, 将前两个步骤获得的参数作为初始值, 构建目标函数, 利用Levenberg-Marquardt算法同时优化光学参数和畸变系数。开展了仿真实验研究, 并与最小二乘法和Samman法的标定结果做了对比, 结果表明: 提出的方法能够很好地实现星敏感器的自主标定。在同等测试条件下, 文中算法获得的最大残差为0.015 pixels, 精度高于其它两种标定方法两个数量级。星敏感器外场实验还表明, 提出的优化方法有效提升了星敏感器的性能。

Calibration methods of traditional star sensors ignore the additional errors from the interaction between optical parameters and distortion coefficients. This paper proposes an autonomous calibration algorithm based on nonlinear optimization to overcome the problems mentioned above. Firstly, the algorithm ignores the distortion to construct a target function, and the Levenberg-Marquardt nonlinear optimization algorithm is used to optimize the optical parameters of the star sensor. Then, the optimized optical parameter estimation iss used as the ideal value, and the lens distortion coefficient of the camera is estimated by the linear least square method. Finally, the parameters obtained by the first two steps are used as initial values to construct the target function, and the optical parameters and distortion coefficients are optimized by using Levenberg-Marquardt algorithm. Simulation and comparison experiments are performed in combination with least square method and Samman method, and results show that the maximum residual obtained by the algorithm is 0.015 pixels under the same test condition, and the accuracy is higher two orders of magnitude than that of the other two calibration methods. Moreover, the field experiments show that the proposed method effectively improves the performance of star sensors.