The Error in Calculated Distance due to the propagation of Positions Error

Abstract

It is known that distance can be measured directly using the instruments of distance measurement, or indirectly using the coordinates of two edge points using the popular Pythagorean formula. In most of the geomatics engineering studies, the error in distances is expressed by the uncertainty of the direct measured distances only, while there is not enough studies that highlight the error in a computed distance. This paper presents the error in distance in a novel formulated approach, which considers the planimetric position error in both edges of the computed distance, to determine the error in that distance. Furthermore, the research concludes that the size and direction of error ellipse at edge points and the azimuth of the distance, are the main factors that combine to define the value of error in those distances that are measured indirectly.