Path and travel time inference from GPS probe vehicle data

We consider the problem of estimating real-time traffic conditions from sparse, noisy GPS probe vehicle data. We specifically address arterial roads, which are also known as the secondary road network (highways are considered the primary road network). We consider several estimation problems: historical traffic patterns, real-time traffic conditions, and forecasting future traffic conditions. We assume that the data available for these estimation problems is a small set of sparsely traced vehicle trajectories, which represents a small fraction of the total vehicle flow through the network. We present an expectation maximization algorithm that simultaneously learns the likely paths taken by probe vehicles as well as the travel time distributions through the network. A case study using data from San Francisco taxis is used to illustrate the performance of the algorithm.