Determination of the point coordinates in 2D geodetic network solution using methods of reference and transition point indicators

Abstract

A new algorithm for determining of the point coordinates in two-dimensional space in geodetic network solution is presented. Geodetic network solution should be understood as a system which consists of reference points, transition points, observations (distances) and the unknown coordinates of the point to be determined. The definition of a transition point indicator with regard to the determined point is introduced. Transition point indicator definition is based on the reference point indicator definitions developed by the author. With the use of definitions of these point indicators, there is a solution for the sought point in geodetic network solution. The direct solution without application of the least squares method is derived. In the proposed solution there is no need to know the initial approximate location of the determined point, nor the coordinates of the transition points. In this article the basic principles of the methods for solving the positioning problem in geodetic network are presented, and the formulas and their derivation are given. The numerical example with simulated data and proof confirm the correct performance of the proposed algorithm. The presented method should be tested with real measurements in many areas of positioning and navigation as well.