The author provides information about the search methods of adjustment and assessment of the elementary geodetic constructions accuracy on the example of a geodesic triangle under various initial conditions. An algorithm for combining Powell and DSC search methods used to solve the problem posed in the article is given. To equalize the geodesic constructions under consideration by the search method, a program for finding the minimum of the objective function is made, it implements the algorithm described in the article. This program works in the Microsoft Excel format as a macro recorded in the VBA language. Examples of equalization calculations are given. Accuracy assessment of the adjustment results by the search method of the geodesic triangle under different initial conditions is performed. The obtained adjustment results and accuracy estimates are compared with the calculations performed in the NW program by Professor Kougiya V. A. confirmed the correctness of the search method application.

The accuracy of determining the points’ position through the free stationing method is estimated. At performing alignment work, surveying facades, executive surveys, and geodetic monitoring of buildings and structures, the method of free stationing with an electronic total station installed in any suitable place and determining its position by serif, and then using the polar method, defi ning the coordinates of the determined point is considered. The accuracy assessment is identifi ed using the formulas of calculating the mean square error for the direct and reverse angular serifs, as well as for linear ones. The authors propose algorithms of accuracy evaluation for the located point positions with non-fi xed stationing method based on the parametric adjustment, and searching ones, at the same time the algorithms shall provide adjustment by considering or ignoring the errors in the input data. To determine the mean square error of the standing point’s position and the determined points according to the results of adjustment by the free stationing method, fi eld experimental studies were carried out. Numerical examples of accuracy evaluation are provided. The compliance of the adjustment results and root-mean-square errors will mean the validity of the proposed algorithms and accuracy of the performed survey.

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.

General idea of the search method is provided. An information flowchart explaining themethod is presented. Formulas for evaluating the project of a geodetic network using the search method based on the undistorted model are given. The sequence of the mentioned design algorithm based on the undistorted model is developed. A computer program for evaluating the project in Visual Basic was compiled. The design and evaluation of the project of two networks, a triangulation geodetic and the one built according to the free stationing scheme was made. Both networks were constructed using the search method of nonlinear programming based on the undistorted model. The results of the evaluation of the triangulation network project coincided with those performed by the classical parametric method, which confirmed the correctness of the proposed algorithm for designing a geodetic network using the search method. The full weight matrix of coordinates of the defined points was obtained, and the average square error of the position of the weakest point in the network calculated.

The authors consider the possibility of using the search method to perform pseudo-rotation of matrices at equalizing free geodetic networks. Two methods of pseudo-circulation of matrices are proposed