中文摘要：

为了科学、准确地估计曲线位置误差以及曲线上任一点精度,使其精度满足工程建设需要和GIS产品质量要求,把曲线分为三类：圆曲线、缓和曲线和拟合曲线,分别研究其位置误差的函数表达以及精度方差矩阵。将曲线上的点表达成函数形式,然后求出所考察点与已知量的微分关系,取加权平均得到其位置误差,应用协方差传播律得到精度的方差矩阵。对三种曲线的研究结果表明,影响位置误差及其精度的因素主要是已知点精度、所求点与已知点的距离和微分系数,为消除和控制误差以及提高精度提供了方法。

英文摘要：

In order to scientifically,accurately estimate the curve position error and the precision of any point on a curve,and to meet the requirement of engineering construction and GIS products quality,the curves are divided into three categories： a circular curve,a transition curve,and a fitting curve respectively,and its position error function expression and accuracy of a covariance matrix are studied. The points on the curve expresses as a function form,then the differential relationship between the point with known quantity are found out,and the position error through taking the weighted average is obtained,and the accuracy of a variance matrix through the covariance propagation is attained. It can also find out the influence factors of position error and accuracy that are known quantity,distance with a known point and differential coefficients through the analysis of the research on three kinds of curve results,and provides methods and measures so as to eliminate and control error and improve accuracy.