Inversion of matrix through the search method at equalizing geodetic networks

Abstract

The theoretical substantiation of matrix inversion by the search method of nonlinear programming is given for equalizing and evaluating the accuracy of geodetic networks’ elements. A theorem on the uniqueness of the extremum point and its corollary (also a remark to the latter) are formulated and proved with minimizing the objective function by the search method at performing matrix inversion. A step-by-step algorithm for matrix conversion by the search method was compiled. The approbation of the developed algorithm was carried out when equalizing and evaluating the geodetic network elements’ accuracy, taking into account the errors of the source data. The correctness of the proposed solutions is confirmed by coinciding the covariance matrix of measurement errors results reversal and that of unknowns’ coefficients normal equations with the calculations performed by the MOBR function in Microsoft Excel, as well as the coincidence of the equalization results and evaluation of the geodetic network’s elements accuracy by the search method with similar calculations by parametric method in the NW program by Prof. V. A. Kougiya.