Estimating continuous highway vertical alignment using the least-squares method

Abstract

Highway profile information may not be available or may not be up to date, especially for old highways. In these cases, profile data are collected using global positioning systems (GPS) or by extracting them from digital images. This paper presents an optimization model for estimating the parameters of continuous vertical alignments, involving multiple parabolic vertical curves that best fit existing highway profile data using the least-squares method. The optimization involves two levels: single-curve optimization and multiple-curve optimization. The former is used to obtain the approximate length of each vertical curve based on the approximate tangent parameters determined from the outline controlling points. The latter is used to obtain the global optimal parameters for tangents and vertical curves. The model is validated and applied using actual data of a vertical alignment. The proposed model presents a useful extension to existing methods for estimating simple vertical alignments and therefore should be of interest to highway engineering professionals.