  Modeling stochastic traffic behaviors at the microscopic level, such as
car-following and lane-changing, is a crucial task to understand the
interactions between individual vehicles in traffic streams. Leveraging a
recently developed theory named physics regularized Gaussian process (PRGP),
this study presents a stochastic microscopic traffic model that can capture the
randomness and measure errors in the real world. Physical knowledge from
classical car-following models is converted as physics regularizers, in the
form of shadow Gaussian process (GP), of a multivariate PRGP for improving the
modeling accuracy. More specifically, a Bayesian inference algorithm is
developed to estimate the mean and kernel of GPs, and an enhanced latent force
model is formulated to encode physical knowledge into stochastic processes.
Also, based on the posterior regularization inference framework, an efficient
stochastic optimization algorithm is developed to maximize the evidence
lower-bound of the system likelihood. To evaluate the performance of the
proposed models, this study conducts empirical studies on real-world vehicle
trajectories from the NGSIM dataset. Since one unique feature of the proposed
framework is the capability of capturing both car-following and lane-changing
behaviors with one single model, numerical tests are carried out with two
separated datasets, one contains lane-changing maneuvers and the other doesn't.
The results show the proposed method outperforms the previous influential
methods in estimation precision.
