On The Integration and Evaluation of Vertical Control Information and Uncertainties in Leveling Networks Using Least Squares Modeling (University of Khartoum Engineering Journal, 2022)
Proper integration and evaluation of an existing vertical control information with the adjustment of a new leveling network require a stepwise approach that could reveal the hidden aspects of their uncertainties or stochastic properties. The general use of the control information as fixed quantities in the adjustment of the leveling networks is a major flaw. To this end, the fundamental concepts of least squares solutions offer a flexible and a rich framework for proper integration and modeling of control information and their uncertainty for new leveling networks. This paper provides a comprehensive review and analysis of a workflow that can be used to integrate and evaluate the existing control information or benchmarks to a new leveling network. In particular, this paper exploits three different approaches of least squares solutions to integrate and evaluate the stochastic properties of the existing control information and observations that belong to a new network. First, ordinary least squares solution, which constrained by Gauss-Markov model, was exploited to depict the normal practice of leveling networks adjustment in which the control information will be introduced as constant or fixed values. Second, least squares solution with pseudo observations was exploited for proper integration of control information and their stochastic properties. Third, free-network least squares solution was exploited as a mechanism to separate and quantify the stochastic properties of the observations from the ones that will be associated with the control information. Through the use of a numerical example, this paper offers some new perspectives and a detailed analysis that explains the interplay between the different aspects of least squares solutions for the integration and evaluation of vertical control information and their uncertainties with new leveling networks.
Keywords: Leveling Networks; Control Information; Uncertainty; Least Squares Modeling