Multivariate time-varying Kalman filter approach for cycle-based maximum queue length estimation

Abstract

Real-time queue length is a crucial information, increasingly needed for signal operation and signal optimization purposes. This paper proposes a novel multivariate time-varying Kalman filter approach to estimate the cycle-based maximum queue lengths in real-time by only using high-resolution vehicle loop detector data and signal timing data. The modeling framework builds on state changing points that can be identified at detector site and shockwave theory that models the propagation of traffic states in the space–time domain. The times at which traffic states change at the detector site, known as break points (e.g., free flow to jam condition, jam to saturation condition, etc.) are identified using high resolution detector data and the end of the queue is estimated using linear models that build on the shockwave theory. Nevertheless, this deterministic approach, which is previously proposed in the literature, does not account for measurements errors associated with traffic state changing points or the assumptions in the shockwave theory. Therefore, we propose a multivariate time-varying Kalman filter approach to produce a robust estimate for the cycle-based maximum queue length in both undersaturated and oversaturated conditions. Further, the developed algorithm can estimate the residual queue length and inform its occurrence in case of oversaturation. The proposed methodology can easily be adapted in practice, as it relies solely on measurements from a single loop detector that may be located close to the stop line.