在多星矢量定位中,由本地坐标系中的光电探测器拍摄到的多星矢量数据需要变换到赤道坐标系中,并与赤道坐标系中的多星矢量数据进行匹配,当匹配误差达到最小时,根据变换矩阵即可确定舰位和航向.由于存在测量误差,因此不可能精确匹配.通过与点模式匹配问题类比,给出了一个求取两组星矢量之间最佳变换矩阵的算法,该算法使匹配误差在均方根意义下达到最小并且其计算复杂性仅为O(n),从而提高了天文定位的精度以及天文定位系统的反应速度.

In the process of multi-star vector celestial position, the multi-star vector data captured by local electro-optic detector should be transformed to the equatorial coordinate system and matched with the corresponding multi-star vector data in the equatorial coordinate system. When the matching error gets its minimum, the location and course of the naval ship can be determined according to the transforming matrix. Exact matching can’t be carried out since there are inevitable measurement errors. Compared with the problem of point patterns matching, an algorithm for computing the best transforming matrix between two groups of star vectors is given. The algorithm can get results with minimal matching error with regard to the root-mean-square and its computational complexity is O(n). Based on this, the precision of celestial position and the response of the celestial position system will be improved.