Travel-Time Estimation by Cubic Hermite Curve

Abstract

Travel time is a measure of time taken to travel from one place to another. Global Positioning System (GPS) navigation applications such as Waze and Google Maps are easily accessible presently and allow users to plan a route based on travel time from one place to another. However, these applications can only estimate general travel time based on a vehicle’s total distance and average safe speed without considering route curvature. A parametric cubic curve has shown a potential result in travel-time estimation through geometric properties. In this paper, travel time has been estimated using the curvature value obtained from the Hermite Interpolation curve fitted to each section of the selected road. Design speed is determined from the curvature value, and thus an algorithm for travel-time estimation incorporating initial driving information is developed. The proposed method’s accuracy was compared to the existing method’s accuracy using a real-life driving test. This comparison demonstrated that the proposed method estimates travel time more accurately than Google Maps and Waze. Future study can further improve the estimation by embedding traffic data into the algorithm.

Comparison of Geometric-based Travel Time Prediction between Cars and Trucks

“…There are various ways to estimate travel time such as using historical data [1][2][3], traffic data [4][5][6][7], machine learning [8][9][10] and road geometry [11]. In many modern navigation systems, all types of data are used together [12].…”

Cubic Trigonometric Hermite Interpolation Curve: Construction, Properties, and Shape Optimization

“…It is well known that cubic Hermite interpolation curve [1] is a common model to construct interpolation curves in engineering, and it has been widely applied in practical engineering problems [2][3][4][5]. However, cubic Hermite interpolation curve has three shortcomings: the first is that it only achieves C 1 continuity, so it cannot meet some engineering problems with better requirements for smoothness; the second is that its shape would be fixed once the interpolation conditions are given, so it cannot meet some engineering problems requiring high flexibility in shape adjustment; the last is that it cannot accurately represent some common engineering curves.…”