Multiple circle intersections. An adjustment problem for observations in typical geodetic problems

Abstract The proposed research problem involves devising a complete numerical procedure for adjusting a distance-distance intersection. The objective of the problem is to find the optimum point of intersection for several circles, where the radii are the results of survey measurements. Two alternative methods are proposed: adjusting the radius lengths as indirect observations and adjusting the individual intersection point coordinates as direct pseudo-observations. Each method involves assessing the location accuracy of the intersected point. The derived equations were tested numerically on practical examples. The devised procedures will be integrated into an exhaustive numerical algorithm for diverse surveying problems that can be easily reduced to multiple distance-distance intersections.