Low-dimensional estimation and prediction framework for description of the oscillatory traffic dynamics

Large majority of control methodologies used in traffic applications require short-time prediction of the environment. For instance, in widely-used Model Predictive Control [1] employed to reduce fuel and energy consumption of vehicles in a platoon, information about future velocity profiles of leading vehicles is necessary. In such case, the dynamic model should provide information more detailed than prediction of averaged and global quantities. Additionally, if the control input is to be applied at high-frequencies, traffic model must be solved in a short period of time. We propose a novel framework which addresses aforementioned problems by estimating the vehicle velocity at any location in the domain based on the real-time information from induction loops downstream. Additionally, our formulation is linear and low-dimensional (i.e. consists of few degrees of freedom) meaning that the estimation can be executed at high frequencies. First a mapping is constructed from velocities at discrete locations to the smooth continuous field, which is subsequently projected onto its most significant principal components. Next, current state of such system is estimated using Kalman filter by combining the linear, wave-like dynamics of the traffic with the instantaneous information provided by induction loops. Short-term traffic prediction is then achieved by integration of the model forward in time. The proxy methodology is validated using SUMO simulation on the test case of the vehicles approaching a traffic junction. The performance is evaluated based on sampling reconstructed continuous waveform at the locations and timestamps of the vehicles in the reference data and calculating velocity errors. Separate cases are considered where drivers follow Intelligent Driver Model perfectly and with varying levels of uncertainty.