Functional Models and New Stochastic Model in Combined Leveling Nets

Abstract

The aim of this study is to improve functional models and to form a new stochastic model that takes into account both different measurement methods and important sources of errors affecting the accuracy of the measurements in a combined leveling net measured by different instruments and measurement methods. In this study, three functional models are explained. In addition, four well-known stochastic models and a new stochastic model are presented. Two types of unknowns are used in the least-squares adjustment of functional models. One of them is the scale factor, and the other is the parameter of refraction and deviation of the plumb line. Four criteria are explained to examine the functional old and new stochastic models. The first criterion is whether or not the adjustment gives reasonable results. The other criteria are the functional model test, stochastic model test, homogeneity, and mean accuracy test. To achieve the objectives stated earlier, a leveling net located in and around Istanbul, Turkey, is used, consisting of 81 benchmarks and 76 lines. Five lines are measured using both reciprocal trigonometric leveling and valley crossing leveling. The rest are measured by the precise leveling method. The net is adjusted using the free adjustment approach along with stochastic models, which are known and suggested.