Platoon Trajectory Reconstruction with Conflict Resolution Using Semidefinite Relaxation

The quality of trajectory data plays a crucial role in the investigation of microscopic traffic flow. However, the challenge of effectively and automatically eliminating false positive collisions from the measured data still remains an unsolved problem. Firstly, this paper formulates the problem of reconstructing multi-vehicle trajectories as a nonconvex quadratic constraint quadratic programming (QCQP) problem. Subsequently, it derives the equivalent semidefinite programming (SDP) problem and develops a semidefinite relaxation technique to e·fficiently obtain the global minimum of the relaxed problem. We then apply a randomization method to obtain a feasible near-optimal solution to the original problem. The proposed approach is validated through experiments conducted on the NGSIM I–80 camera 6 lane 5 data, and the results of these experiments demonstrate that the unreasonable vehicle dynamics are removed and the platoon inconsistency decreased from 0.622% to 0.268% in the experimental data.