Estimation of space-speed profiles: A functional approach using smoothing splines

Individual space-speed profiles are very informative to study drivers behavior and their road usage. Due to uncertainties in the measurements of position and speed from sensors, there is need of use a smoothing procedure in order to estimate these space-speed profiles. The purpose of this study is to propose a smoothing method based on a functional approach. This approach take inspiration from Functional Data Analysis, a statistical domain that has developed recently. So, we define and study some properties of the functional space of space speed profiles. Then, due to the correspondence between speed and position (and implicitly time), we prove that a change of study area (distance vs time) is more appropriate and leads to a smoothing problem under monotonicity constraint. An estimation method of monotone smoothing spline is used and tested with simulated data.