基于卡尔曼滤波的星敏感器在轨校准方法

根据星敏感器光学镜头以径向畸变为主的特点,采用一阶径向畸变模型,利用摄像机标定中的径向排列约束(RAC),对其外部姿态和内参数进行在轨校准。以采集到的星点的图像坐标和对应导航星在天球坐标系下的赤经、赤纬信息作为滤波器的输入,外部姿态和内参数作为输出,构造相应的状态方程和观测方程,进行两次卡尔曼滤波迭代,结果作为校准参数的最优估计。仿真实验表明:本方法能消除内部参数与外部参数的耦合,校准过程不依赖外部姿态,且状态方程和观测方程均为线性方程,满足卡尔曼滤波迭代的最优条件,能够精确估计出星敏感器内外参数,在星点成像位置噪声标准差为0.05像素时,校准后x、y方向上的平均误差分别为0.044像素和0.049像素。

On-orbit Calibration of Star Sensor Based on Kalman Filter

An on-orbit calibration method of star sensor based on Kalman filter is proposed in this article. Considering the distortion feature of most optical camera lens, internal and external parameters of star sensor are calibrated separately using Kalman filter with first-order radial distortion. Taking the image coordinates and the corresponding celestial coordinates of observed star points as the filter inputs and taking the estimated value of the internal and external star sensor camera parameters as the filter outputs, the optimized value of the internal and external parameters are obtained with Kalman filter algorithm, while state equation and observation equation for Kalman filter are established based on radial alignment constraint (RAC) which is widely used in camera calibration of computer vision. The simulation results indicate that this method which is independent on external attitudes can eliminate the coupling between external parameters and internal parameters effectively, and it also satisfies the optimal qualification demanded by Kalman filter that both state equation and observation equation are linear. When the standard deviation of star positional noise is set to 0.05 pixels, the internal and external parameters are correctly obtained and the residual errors can reach 0.044 pixel on average in x direction and 0.049 pixel in y direction respectively.