STUDY OF THE ALGORITHM OF PSEUDONORMAL OPTIMIZATION ON THE STABILITY OF THE SOLUTION OF THE EQUATION PROBLEM AND THE ESTIMATION OF THE ACCURACY

Abstract

In geodesic practice, when designing and adjusting geodetic networks for various purposes on a computer, it is necessary to solve poorly conditioned systems of linear normal equations. In such systems, the determinant of the matrix of equations tends to zero, so the application of the least squares method leads to large distortions of the estimated parameters. Moreover, in such situations, for the least squares algorithm, a slight distortion of the input data leads to unacceptably large distortions of the final results of the equalization and accuracy estimation. In this regard, the application of the pseudonormal optimization method is proposed. The presented work is devoted to the study of the stability of the solution of the adjustment task and the estimation of accuracy obtained on the basis of the pseudonormal optimization method. The novelty is the obtained algorithm for estimating the relative error of the pseudonormal optimization method. A comparative analysis of two competing processing methods was performed for different network models. The results of experimental studies and their analysis have shown the advantage of the pseudonormal optimization method over the least squares method.