Fitting Composite Horizontal Curves Using the Total Least-Squares Method

The parameters of horizontal curves are sometimes missing or need to be updated using observed x and y coordinate data. The observed data for existing alignments may be obtained using global positioning systems (GPS) or extracted from digital imagery. Previous methods have addressed the case where only the circular or the transition curves are estimated. This paper presents an optimisation model for composite horizontal curves that simultaneously fits the circular curve, its transition curves and the two tangents using the total least-squares method. The objective function minimises the squared deviations between the observed and predicted values. The model can be applied to fitting single or multiple composite horizontal curves. Since the model is nonlinear and non-convex, a close initial solution is first developed and then used to obtain the global optimal solution. The model is validated and applied using actual data of a horizontal alignment. The proposed model presents an important extension to existing methods for estimating horizontal alignments and therefore should be of interest to surveying professionals.