Using probe vehicle trajectories in stop-and-go waves for inferring unobserved vehicles

Data from vehicles instrumented with GPS or other localization technologies are increasingly becoming widely available due to the investments in Connected and Automated Vehicles (CAVs) and the prevalence of personal mobile devices such as smartphones. Tracking or trajectory data from these probe vehicles are already being used in practice for travel time or speed estimation and for monitoring network conditions. However, there has been limited work on extracting other critical traffic flow variables, in particular density and flow, from probe data. This paper presents a microscopic approach (akin to car-following) for inferring the number of unobserved vehicles in between a set of probe vehicles in the traffic stream. In particular, we develop algorithms to extract and exploit the somewhat regular patterns in the trajectories when the probe vehicles travel through stop-and-go waves in congested traffic. Using certain critical points of trajectories as the input, the number of unobserved vehicles between consecutive probes are then estimated through a Naïve Bayes model. The parameters needed for the Naïve Bayes include means and standard deviations for the probability density functions (pdfs) for the distance headways between vehicles. These parameters are estimated through supervised as well as unsupervised learning methods. The proposed ideas are tested based on the trajectory data collected from US 101 and I-80 in California for the FHWA's NGSIM (next generation simulation) project. Under the dense traffic conditions analyzed, the results show that the number of unobserved vehicles between two probes can be predicted with an accuracy of ±1 vehicle almost always.