On The Integration and Evaluation of Vertical Control Information and Uncertainties in Leveling Networks Using Least Squares Modeling

Gamal H. Seedahmed
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Abstract

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.
基于最小二乘模型的水准网垂直控制信息与不确定性集成与评价
将现有的垂直控制信息与新的水准网的平差进行适当的整合和评估需要一种逐步的方法,这种方法可以揭示其不确定性或随机特性的隐藏方面。在水准网平差中,一般将控制信息作为固定量使用是一个重大缺陷。为此,最小二乘解决方案的基本概念提供了一个灵活和丰富的框架,为新的水平网络的控制信息及其不确定性的适当集成和建模。本文提供了一个工作流程的全面回顾和分析,该工作流程可用于集成和评估现有的控制信息或新的水平网络的基准。特别地,本文利用三种不同的最小二乘解方法来整合和评估属于新网络的现有控制信息和观测值的随机特性。首先,利用高斯-马尔可夫模型约束下的普通最小二乘解来描述水准网平差的一般做法,其中控制信息将作为常量或固定值引入。其次,利用带伪观测值的最小二乘解对控制信息及其随机特性进行适当整合。第三,利用自由网络最小二乘解作为一种机制来分离和量化与控制信息相关的观测值的随机特性。本文通过一个数值算例,提供了一些新的观点,并详细分析了新水准网中垂直控制信息整合与评估的最小二乘解各方面之间的相互作用及其不确定性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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