顾及已知点精度的自由设站算法及精度分析

Precision analysis and algorithm of free-station positioning considering precision of known points

基于全站仪自由设站方式,在考虑已知点精度的基础上,对全站仪方向及距离观测值分别列出误差方程,采用最小二乘配置原理,得出了适应于2个及以上已知点的全站仪自由设站测站坐标、定向角及精度计算模型,利用测站坐标、定向角以及它们的协方差矩阵,进一步给出了细部点的坐标及精度解算模型.对测站精度、细部点精度分布规律进行了分析,结果表明:测站精度和细部点精度均呈同心圆向外衰减,圆中心在已知点的加权平均中心上,半径决定于已知点的精度、数量与分布;测站精度与测站的交会角几乎没有关系,细部点精度与测站的位置几乎无关,且可能高于测站精度.实例验证的结果表明,实测结果与理论分析的结果是一致的.

Considering the precision of known points, the direction and distance observation error equations which are acquired by free station are presented. According to the least-square collocation principle, the algorithm of station coordinates and orientation angle and their precision is got. Moreover, the model to solve the detail coordinates and their precision is discussed by using covariance matrix. Precisions of the station and detail points are analyzed. It is concluded that the precision of these points is attenuated equidistantly as concentric circles. Its center is the weighted average of the coordinates of known points with the radius determined by the precision, the quantity and the distribution of known points. The precision of station points is almost independent of intersection angle, and the precision of known points is almost independent of station point. In some circumstance, the detail points may be more precise. These theoretical results are found to be consistent with the experiment data.