椭圆形地理实体定位中的平差问题

An adjustment problem about position and orientation of ellipse geomatic entity

在地理实体中,有很多是椭圆或圆形的,大部分实体的中心无法到达或无法判定,必须对椭圆形实体边界进行测量,然后确定椭圆的中心位置(椭圆的定位)、长轴和短轴长度(椭圆形状)及长轴方向(椭圆的定向)。当测量其5个边界点,可惟一解出定位和定向参数,超过5个测点时,就产生平差问题。本文推导出一套椭圆定位和定向的直接计算公式,并提出平差模型,通过实例论证该模型的正确性和实用性。

The shape of many geomatic entities is elliptic or round style. Their centre can＇ t be arrived or determined. Series points on boundary of elliptic geomatic entity must be measured. Then the center, the length of major axis and minor axis and the orientation of Elliptic entity can be determined, which is called ellipse position and orientation（EPO）. There are five parameters on EPO. The position parameters and orientation parameter are only determined when five boundary points are collected. When more than five boundary points are ovserved, the adjustment problem will be presented. In this paper the direct calculation formulas of EPO are derived and the adjustment model of EPO is given too. In conclusion, instance demonstrates that the method is right and practical.