Design of an adaptive maximum likelihood estimator for key parameters in macroscopic traffic flow model based on expectation maximum algorithm

A large number of freeway networks can be described by non-linear, non-Gaussian macroscopic second-order state-space models. One of the most challenging problem in traffic monitoring systems is estimation of key parameters in traffic flow model including critical density, free flow speed and exponent of a motorway segments, which are continuously subject to changes over time due to traffic conditions (traffic composition, incidents, ) and environmental factors (dense fog, strong wind, snow, ) and missing data regarding to problems in distributed sensor network and communication links. These parameters have critical effects on the performance of the traffic control strategies and applications such as traffic control, ramp metering, incident management and many other applications in intelligent transportation systems (ITS). So, they must be estimated accurate and on-line. Here, in the first step, mentioned parameters will be estimated offline using all available measured data by implementing maximum likelihood method via the employment of an expectation maximisation (EM) algorithm. Then proposed approaches will be developed to construct an adaptive estimator for calibrating online the static parameters in non-linear non-Gaussian state space model of traffic flow. These approaches are asymptotic and statistical techniques and are based on online EM-type algorithms. Unlike to recently proposed standard sequential Monte Carlo (SMC) methods, these algorithms do not degenerate over time. To approximate first and second derivatives of optimal filter, required in these approaches, without sticking in analytical complexities, here EM algorithm has been implemented based on particle filters and smoothers. Two convincing simulation results for two set of field traffic data from the Berkeley Highway Laboratory (BHL) and Regional Traffic Management Center (RTMC), a part of Minnesota Department of Transportation (MnDOT), are presented to demonstrate the effectiveness of the propos- - ed approach.