Study on the rigorous accuracy of any point on a linear element

In order to obtain the rigorous accuracy of any point on the straight line element, based on existing research, this article considers the error of the straight line element and the error of any point to its end point of the straight line element, attempts to discuss the accuracy calculation of any point on the straight line element in three different situations, and through case analysis, compares the position covariance matrix of any point on the straight line element in three situations and draws its error ellipse using MATLAB programming. Finally, different accuracy sizes and different error ellipses are obtained. This research has certain guiding significance and role for error calculation in precision engineering measurement, such as large bridges or large through projects.