The Development of Maximum Likelihood Estimation Approaches for Adaptive Estimation of Free Speed and Critical Density in Vehicle Freeways

The performance of many traffic control strategies depends on how much the traffic flow models are accurately calibrated. One of the most applicable traffic flow model in traffic control and management is LWR or METANET model. Practically, key parameters in LWR model, including free flow speed and critical density, are parameterized using flow and speed measurements gathered by inductive loop detectors and Closed-Circuit TV.  The challenging problem here is continuous changes in these parameters due to traffic conditions (traffic composition, incidents) and environmental factors (dense fog, strong wind, snow) and missing data. In this paper Maximum Likelihood approaches are developed to the LWR model identification while inaccurate observations are available at the traffic control center. A Maximum Likelihood method is accomplished via the employment of an Expectation Maximization algorithm. To approximate first and second derivatives of optimal filter without sticking in analytical complexities, The EM algorithm is implemented based on particle filters and smoothers. Two convincing simulation results for two sets of field traffic data are used to demonstrate the effectiveness of the proposed approaches.