Modal Activity-Based Stochastic Model for Estimating Vehicle Trajectories from Sparse Mobile Sensor Data

Probe vehicles that measure position and speed have emerged as a promising tool for traffic data collection and performance measurement, but the sampling rates of most probe vehicle sensor data available today are low (ranging from 10 to 60 s per sample), and the data coverage is limited. Therefore, it is challenging to accurately estimate the vehicle dynamic states in both space and time based on these sparse mobile sensor data. In this paper, a stochastic model is proposed to estimate the second-by-second vehicle speed trajectories by examining all possible sequences of modal activities (i.e., acceleration, deceleration, cruising, and idling) between consecutive data points from sparse position and speed measurements. The likelihood of occurrence of each sequential pattern is first quantified by mode-specific a priori distributions. The vehicle dynamic state probability is then formulated as the product of probabilities for multiple independent events. Therefore, a detailed vehicle speed trajectory can be reconstructed using the optimal modal activity sequence, which maximizes the likelihood. The proposed model is calibrated and validated using the Next-Generation SIMulation dataset. The results show the substantial improvements on the accuracy of estimated vehicle trajectories compared with a baseline method based on linear interpolation. The proposed model is applied to a large-scale vehicle activity dataset to demonstrate the estimation of hourly traffic delay variation.