Traffic State Estimation with Stochastic Three-Detector Modeling Considering Heteroscedasticity

Abstract

Advancements in sensor, communication, and computer technologies have significantly enhanced traffic detection methods, providing high-quality and reliable data for traffic management. However, budgetary constraints still prevent full network coverage of traffic detectors, which necessitates the maximization of available detection data to accurately estimate overall traffic flow states. This paper extends Newell’s deterministic three-detector model to a stochastic framework to estimate traffic stream states while accounting for heteroscedasticity. It is widely acknowledged that errors exist in traffic state estimations (TSEs) made by loop detectors. The relevant literature typically assumes these error terms to be normally distributed, neglecting the inherent characteristic that error variance is time-dependent. In this work, considering that the detector error has heteroscedasticity in terms of different time periods, we aim to enhance the accuracy of the estimation model by developing a new stochastic three-detector model. More specifically, a dynamic linear model (DLM) is utilized to analyze the heteroscedasticity of stochastic terms and a linear mean-variance function is established to represent the mean-variance relationship and overcome the homoscedasticity issue. We employ the traffic flow data set collected from performance measurement system (PeMS) to validate our proposed methodology. In contrast to extant studies on both deterministic and stochastic three-detector models, the methodology advanced herein, which incorporates heteroscedasticity into a stochastic three-detector framework, markedly enhances the precision in estimating the likelihood of free-flow and congested states at any arbitrary location within a road segment.