On the issue of multi-group adjustment of filling triangulation by the method of indirect observations

Abstract

The method of multi-group equalization by the method of indirect observations, proposed by I. Yu. Pranis-Pranevich, has now received very wide application in the Soviet Union in equilibration of large filling networks of class II. This method is not entirely rigorous and leads to results somewhat different from the results obtained with strict joint equalization of the network by the method of indirect observations in corrections to directions. In this article, we will give a quantitative estimate of the distortions in the network arising from the non-rigor of the multi-group equalization method, and we will show that without significantly complicating the equalization calculations, these distortions can be almost completely eliminated.