基于几何覆盖的导航星视场构造算法

由导航星表构造导航星匹配模式是星图匹配、识别的最关键步骤。为了从根本上能保证星图识别模式的完备性,提出了构造导航星视场的方法。从导航星表中任一颗星开始,依次找到两两角距小于FOV的星,构成1颗星、2颗星…m颗星的全部子集(子集P)。以子集P中心的视轴为基准,取两倍于视场的导航星子集Q(Q包含P)。把Q中的每一颗星投影到星敏感器像平面,形成点列子集Q。视场的构造就可以表述为平面上点集的几何覆盖问题。对每一个子集P来说,先计算其最小覆盖圆,若其半径小于视场在像平面的投影值(R),则计算点列子集Q删除P后的Voronoi图,这样就可求出包含点列子集P的最大空圆;若其半径大于R,则点列子集P为一个导航星视场。给出了由20颗导航星生成的124个视场,并与Monte Carlo 20万次随机生成的视场作了比较。结果证明了该算法是有效的、实用的。

Algorithm constructed the field of view by geometric covering

The key step to match and identify the star pattern is to construct the field of view(FOV)of the navigation stars.To obtain the full star identification patterns,an algorithm of constructing FOV of navigation stars is proposed.Let P be the set of stars whose angle distances between any twosome are smaller than FOV,to obtain all subset P including one star,two stars,… m stars.Generate the subset Q whose centre bore sight is the same as subset P,is twice the FOV(Q contains P).The stars of subset Q are projected into the image plane of the star sensor,the constructing of FOV may be transformed into a question of geometric covering for the set of points in plane.The minimum covering circle of the subset P is calculated by sorting according to the coordinates of the projected points.If its radius is smaller than the FOV in image plane projection value(R),then,the Voronoi diagram of the subset subtracted P from Q,can be calculated.The largest "empty circle" which contains subset P is obtained,if its radius is larger than R,the subset P is in a single FOV.An example is given,all FOVs of 20 stars are 124,the comparison between 200000 stochastic FOV from Monte Carlo and this method(geometric cover)is made,the result proves that this algorithm is valid.