Simple Algorithm for rigorous least squares solution to levelling networks

Abstract

Simple Algorithm for rigorous least squares solution to Levelling networks

The theoretical and practical aspects of rigorous least squares solution to levelling networks are investigated by asimple algorithm which developed in this work. Experiment indicates that levelling networks data which involve field survey differential leveling observations i.e., difference in heights between the existing benchmark and new established junction points, can be rigorously adjusted without significant increase to the costs as compared to non-rigorous or empirical adjustment methods.

The algorithm is based on the method of variation of coordinates (observation method).

The final output allows a posteriori variance-covariance analysis. It is shown that because of its simplicity, this algorithm provides a universal use capability in ground plane surveying for measuring and computing the adjusted heights of the new established benchmarks which are used for roads, sewage, irrigation, geology and other civil and environmental engineering projects.