Position line and point position error

Abstract

The general theory of position lines and gradients provides greater clarity and simplicity in matters of graphical adjustment and determination of point position errors. In geodesy, when determining the position of the required points on a plane, we directly measure horizontal angles and distances, which can be considered as a function of two variables (coordinates). This measured value of the function corresponds to a certain geometric location of points on the plane - a certain line, which we call the line of position. Let's move on to the point position errors. The position of the projection of a point on the horizontal plane is determined by the intersection of two lines of position of two measured functions. Graphic adjustment using gradients is very useful for repeated trigonometric determinations of moving points, for example in landslide areas, in areas subject to displacement from underground mine workings, etc. Once constructed, the error figure with the found gradients will serve as a convenient means for further studies of the movement of the determined point.