Multiple model stochastic filtering for traffic density estimation on urban arterials

Traffic state estimation plays an important role in Intelligent Transportation Systems (ITS). It provides the latest traffic information to travelers and feedback to signal control systems. The Interactive Multiple Model (IMM) filtering provides a powerful estimation method to deal with the non-differentiable nonlinearity caused by the phase transitions between the under-critical and above-critical traffic density regimes. The IMM filtering also accounts for the uncertainty in the current ‘mode of operation’. In this paper, we develop an enhanced IMM filtering approach to traffic state estimation, with an underlying Cell Transmission Model (CTM) for traffic flow propagation. We improve the IMM filtering with CTM in two ways: (1) We apply two simplifying assumptions that are highly likely to hold in urban roads in incident-free conditions, which makes the computational complexity to grow with the number of cells only polynomially, rather than exponentially as reported in prior work. (2) We apply a novel approach to noise modeling wherein the process noise is explicitly obtained in terms of the randomness in more fundamental quantities (e.g., free-flow speed, maximum flow capacity, etc.), which not only makes noise calibration using real data convenient but also makes the computation of the cross-correlation between the process and measurement noises transparent. However, it leads to ‘process dynamic’ and ‘measurement’ equations that involve multiplier matrices whose elements are random variables rather than deterministic scalars, and hence, standard filtering equations cannot be applied. We derive the appropriate filtering equations from first principles. We calibrate the traffic parameters and the total inflow and outflow on the links using the SCATS loop detector data collected in Melbourne and report significant improvements in accuracy, which is due to the accurate computation of the cross-covariance of process and measurement noises.