Predicting public transit arrival: A nonlinear approach

Arrival/Travel times for public transit exhibit variability on account of factors like seasonality, dwell times at bus stops, traffic signals, travel demand fluctuation etc. The developing world in particular is plagued by additional factors like excess vehicles, poor lane discipline, diverse modes of transport and so on. This renders the bus arrival time prediction (BATP) to be a challenging problem especially in the developing world. A data-driven approach for BATP in real-time is proposed in the current work. We explicitly learn both spatial and temporal correlations in a general (non-linear) fashion, unlike most existing approaches. The real-time BATP is next intelligently reposed as a hidden-state estimation (or inference) problem on a related non-linear dynamical system (NLDS) model. We propose an Extended Kalman Filter (EKF) and Particle Filter (PF) based solution to the above inference problem. We demonstrate utility of this general framework of learning and prediction using (i)support vector regression and (ii)feed-forward ANN to learn spatial and temporal correlations. The EKF based inference under support-vector and feed-forward approximations to the system maps of the associated NLDS model reveals interesting computational structure, which goes beyond the BATP application. Specifically, the Jacobian computation at each step of the EKF can be carried out exactly and efficiently using either (i)forward recursion (ii)backward recursion (back-propagation) under feed-forward approximations. Under support-vector approximation, this Jacobian evaluation is possible in closed form. The effectiveness of the proposed algorithms is illustrated on real field data collected from challenging traffic conditions. Our experiments demonstrate similar prediction performance of both the proposed EKF and PF while they outperform diverse existing state-of-art data-driven approaches proposed for the same problem.