Development of a contiguous three-dimensional geometric highway model using historic global positioning system data

An algorithm for estimating a three-dimensional spatial model of roadway geometry from historic Global Position System (GPS) data is presented herein. The historic database of GPS data contains multi-million spatial coordinate triplets of longitude, latitude, and elevation representing 11,000 miles of the Kansas state highway system. The model captures the spatial trajectory of a highway using a series of control points consisting of longitude, latitude and elevation estimated from the historic GPS data. Although several concepts from digital signal processing, optimal estimation and data reduction are applicable to the current problem, the unique structure and error distribution of the historic GPS data prohibit direct application of established methods. A new algorithm is presented that is a variant of a robust least squares technique. Low-order normalized piece-wise polynomials are used as the basis functions. Both the position data and estimates of the first derivative are used in the fitting process to take advantage of the high correlation of the GPS data error. Robust fitting techniques are used to iteratively reweight data points, and estimate bias errors. Control points are calculated from piece-wise polynomial model. Accuracy metrics are calculated that characterize absolute position error, relative position error and error in the first derivative of the spatial model. In comparison with elevation design profiles for three segments of highway, the algorithm produced elevation models with elevation standard deviation of 1.5 feet and grade standard deviation between 0.10 and 0.17 percent.