Kernel Regression for Vehicle Trajectory Reconstruction under Speed and Inter-vehicular Distance Constraints

This work tackles the problem of reconstructing vehicle trajectories with the side information of physical constraints, such as inter-vehicular distance and speed limits. It is notoriously difficult to perform a regression while enforcing these hard constraints on time intervals. Using reproducing kernel Hilbert spaces, we propose a convex reformulation which can be directly implemented in classical solvers such as CVXGEN. Numerical experiments on a simple dataset illustrate the efficiency of the method, especially with sparse and noisy data.