Distributed maximum likelihood estimation for flow and speed density prediction in distributed traffic detectors with Gaussian mixture model assumption

In this study a distributed maximum likelihood estimator (MLE) has been presented to estimate ML function of traffic flow and mean traffic speed in a freeway. This algorithm uses traffic measurements including volume, occupancy and mean speed which gathered by some inductive loop detectors. These traffic detectors (traffic sensors) located in certain distances in the freeway network such that they establish a distributed sensor network (DSN). The presented distributed estimator has employed a distributed expectation maximisation algorithm to calculate MLE. In the E-step of this algorithm, each sensor node independently calculates local sufficient statistics by using local observations. A consensus filter is used to diffuse local sufficient statistics to neighbours and estimate global sufficient statistics in each node. In the M-step of this algorithm, each sensor node uses the estimated global sufficient statistics to update model parameters of the Gaussian mixtures, which can maximise the log-likelihood in the same way as in the standard EM algorithm. As the consensus filter only requires each node to communicate with its neighbours, the distributed algorithm is scalable and robust. A set of field traffic data from Minnesota freeway network has been used to simulate and verify the proposed distributed estimator performance.