Uncertainty in the Back-Calculation of Geometric Parameters of Vertical Curves Obtained with UAV

In existing roads, the geometrical parameters of the alignment are the primary input for safety or geometrical improvement studies. However, the as-built drawings are not always available to obtain geometrical parameters, whereby they must be back-calculated from surveying data. The procedures to back-calculate geometrical parameters of existing roads and fit profile data use parametric methods such as polynomials or explicit functions and nonparametric methods such as splines or smoothers. In smoother-based methods, a usual computing decision is to consider a fixed spacing, one smoothing algorithm, and one set of smoothing parameters to obtain a single set of curvature, deflection, and length (KAL) parameters of vertical curves. Therefore, different values of KAL parameters will be obtained depending on the choice of spacing, smoothing algorithm, and smoothing parameters. This paper aims to study the relative effect in the variability of KAL parameters of a vertical curve, introduced by several spacing combinations, smoothers, and parameters, using data obtained with an unmanned aerial vehicle (UAV). Elevation and slope data were obtained from a digital elevation model every 2, 5, and 10 m. The slope-horizontal distance diagrams were smoothed using single, double, and triple exponential smoothing for different levels, trends, and season parameters. The KAL parameters were back-calculated for each slope-horizontal distance diagram, and the variability analysis was undertaken with boosting regression, multiple analysis of variance, and $k$-nearest neighbor algorithm and tested using receiver operating characteristics (ROC) curves. Results show that the smoothing algorithm and parameters choice affected mainly the $K$ parameter and that the single exponential smoothing algorithm is more suitable than double and triple exponential smoothing algorithms to estimate the KAL parameters.