Real-time estimation of turning movement proportions from partial counts on urban networks

Modern traffic signal control systems require reliable estimates of turning flows in real time to formulate effective control actions, and accommodate disturbances in traffic demand without deteriorating the system performance. The more accurate the estimation is, the more effective the control plan is. Most of the previous research works assumed that a full set of detector counts is available and employed the least-squares methods to produce unbiased estimates of the turning movement proportions. However, in practice, such a dense detector configuration is expensive to install and maintain. Also, the least-squares estimates are not feasible when the travel time between inflows and outflows is significant, or when intervening traffic conditions change the travel time. This study proposes a nonlinear least-square (NLS) approach and a quasi maximum likelihood (QML) approach to recursively estimate turning movement proportions in a network of intersections where only a partial set of detector counts are available. Using large population approximation technique, a class of nonlinear, discrete-time traffic flow models are transformed into a linear state–space model tractable for on-line applications. The quality of estimates is demonstrated by implementing the proposed algorithms with simulation and real data. As a comparison, the NLS estimator shows less bias but with higher variance than the QML estimator. The QML estimator outperforms the NLS estimator in terms of total mean square error, due to an increase in bias being traded for a decrease in variance.