Optimization-based Highway Traffic State Estimation with Bound Guarantees

Abstract

Uncertainty about the system behaviour and the sensor measurements hinders reliable traffic state estimation, affecting various transportation operations, especially traffic control and incident detection. This work proposes a systematic, model-based, network-wide and online optimization methodology to achieve traffic state estimation with bound guarantees in the presence of measurement and modelling uncertainties. In other words, the developed methodology yields upper and lower bounds on each system state at the present time-step, which are guaranteed to contain the true state. The proposed methodology solves two optimization problems for each state (minimization/maximization problem yields lower/upper state bounds) over a moving time horizon, with the unknown terms varying freely in the uncertainty set. The methodology is exploited for highway traffic density estimation with bound guarantees, using the Asymmetric Cell Transmission Model. In this context, three novel algorithms of different characteristics are proposed. The first is a Mixed Integer Linear Programming algorithm that accurately implements the proposed methodology. The second derives the convex hull of the model's nonlinear functions, yielding a Linear Programming formulation. The third is a low-complexity heuristic algorithm that finds density bounds for each cell by only considering currently available density bounds on neighbouring cells. Simulation results examine the effectiveness of the proposed algorithms and demonstrate that each algorithm provides a different level of tradeoff between solution quality and execution time.