L2范式距离的星图识别方法

在Hausdorff距离的基础上，提出一种不依赖于星敏感器的旋转方向和焦距等因素的星图识别方法。在构造Hausdorff距离的数据点集合时，采用基于L2范数对应的相对欧氏距离作为集合元素，解决星敏感器滚动对星图识别的影响；另一方面，由于受星敏感器焦距的影响，星敏感器图像与标准参考图也会存在误差。在构造标准数据点元素时，考虑到如果一个数据点集包含另一个数据点集，在这两个数据点集之间至少有两个数据点之间的L2范式距离是相同的。对L2范式Hausdorff距离进行比例化处理，每个集合中的相对空间距离除以本集合中最小的相对空间距离，构成一种新的数据点集。这种方法不需要对星敏感器图像由于焦距不同进行标定，避免了星敏感器焦距对星图识别的影响。给出了距离的计算公式和实现步骤，并给出了实验结果。结果表明:在星敏感器转动、尺度变换等情况下，该算法可以正确得到星图识别结果，从而获得星敏感器的姿态信息。

Star map recognition method of L2 normal distance

Based on the Hausdorff distance (HD), a star map recognition method was presented that did not depend on the rotation direction and focal length of the star sensor. When constructing the data point set of Hausdorff distance, the relative Euclidean distance corresponding to norm L2 was used as the set element to solve the influence of star sensor rolling angle on star pattern recognition. On the other hand, due to the influence of the focal length of star sensor, there were errors between the star sensor image and the standard reference image. When constructing standard data point elements, if a data point set contained another data point set, the L2 normal distance between at least two data points between the two data point sets was the same. Therefore, the relative distance was scaled, and the relative spatial distance in each set was divided by the smallest relative spatial distance in the set to form a new set of data points. This method was not necessary to calibrate the star sensor image due to different focal lengths influence. The calculation formula, implementation steps and the simulation results were presented. The experimental results show that the algorithm can obtain the star map recognition results correctly and get the attitude information of star sensor in the case of star sensor rotation, scale transformation, etc.