Network-wide speed-flow estimation considering uncertain traffic conditions and sparse multi-type detectors: A KL divergence-based optimization approach

Accurate monitoring and sensing network-wide traffic conditions under uncertainty is vital for addressing urban transportation obstacles and promoting the evolution of intelligent transportation systems (ITS). Owing to fluctuations in traffic demand, traffic conditions exhibit stochastic variations by the time of day and day of the year. The joint estimation of stochastic speed and flow is pivotal in ITS, drawing on the symbiotic relationship between these two variables to furnish comprehensive insights into traffic conditions. Nevertheless, constraints such as budgetary limitations and physical boundaries render the coverage of traffic detectors both sparse and inadequate, thereby complicating the precise assessment of network-wide traffic speeds and flows in uncertain scenarios. To address this challenging problem, this paper proposes a novel network-wide traffic speed-flow estimator (SFE) grounded in the Kullback-Leibler divergence optimization method. This SFE harnesses data derived from sparse multi-type detectors, such as point detectors and automatic vehicle identification sensors. Significantly, it leverages the statistical correlation relationships (i.e., covariance matrix) of the speed and flow between observed and unobserved links to estimate stochastic speed and flow on unobserved links (i.e., the links without traffic detectors). In addition, fundamental diagrams, modeling the interdependence between link speeds and flows, are incorporated as constraints in the proposed SFE. This inclusion markedly diminishes discrepancies and elevates estimation precision relative to individual assessments of speeds and flows. Numerical illustrations, encompassing both simulated and real- world road networks, validate the enhanced performance and applicability of the proposed SFE, suggesting its potential role in augmenting data robustness within ITS.