Abstract：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.

Keyword：circular curve;transition curve;fitting curve;position error;