Using Polar Coordinates to Filter Trajectories Data without Adding Extra Physical Constraints
Résumé
Filtering methods for the position or the speed measurements of the NGSim trajectories dataset are numerous, but specific to the noise resulting of NGSim data collection and processing. The MOCoPo (Measuring and mOdelling COngestion and POllution) collaboration collected more than 10 hours of data with a high resolution camera mounted underneath a helicopter flying almost immobile above a freeway in Grenoble. Along with the post-treatment method, this generates a noise in the position measurement of the center of gravity of the image associated with the vehicle. We present a method classically based on polynomial fitting but where the originality states in using the polar coordinates instead of the Cartesian ones as is usually done. Indeed the radial coordinate capture most of the physics of the act of driving a car: selecting a speed, whereas the polar angle is much more related to the geometry of the road. The method fits the space travelled whose derivative is the real instantaneous speed. This method is developed in two versions: piece-wise constant accelerations or piece-wise linear accelerations. In both cases the root mean square error of the position measurements is of less than 0.4 m. The main advantage of this method is that it provides values of acceleration fully compatible with the physical limits found in the literature, without adding extra constraint.