A functional analysis of speed profiles: Smoothing using derivative information, registration, and speed corridors
Résumé
The knowledge of the actual vehicle speeds on the road network is a very informative component of drivers behavior and their road usage. This information become available with the generalization of probe vehicles and the development of GPS-equipped smartphones which has increased the number of "tracers" likely to refer their position and speed data in real time. In addition, advances in sensors technology leads to large volume of individual space-speed profiles (i.e. speed as function of space) with increasingly fine grids measurements, which requires appropriate methods. The originality of the approach presented in the current paper is to propose a functional analysis of speed profiles, i.e. to treat these objects as functions rather than vectors. This functional analysis begins with a functional modeling of space-speed profiles and the study of mathematical properties of these functions. Then, a smoothing procedure based on spline smoothing is developed. It is shown that this smoothing step leads to a complex nonparametric regression problem that needs to take into account two constraints: the use of the derivative information, and a monotonicity constraint. This paper also presents a methodology to build an aggregated speed profile (average or median), and also speed corridors in order to summarize the information contained in a large set of individual space-speed profiles. This methodology is illustrated on a real data set and is divided in the three following steps: the smoothing step, the registration of speed profiles by the method of landmarks alignment, and the construction of speed corridors by an extension of the classical boxplots to functional data.
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