Estimation of dynamic origin-destination by Gaussian state space model with unknown transition matrix

The dynamic origin-destination (O-D) pattern representing time-dependent trip demands from one place (origin) to another (destination) is amongst the most essential input data for most traffic operational analyses. Historical studies assumed that the transition matrix is known or at least approximately known, which is unrealistic for a real world network. Due to the fact that the number of trips to a specific destination, y, is easy to obtain and the O-D variable, x (path flow based in this research), is not directly observable, a Gaussian state space model is formulated to describe the relationships of x and y, observation equations, and the dynamics of x , state equations with unknown transition matrix. Under the assumption of Gaussian noise terms in the state space model, the distribution of the random transition matrix F is derived. A solution algorithm combining a Gibbs sampler and Kalman filter to tackle the problem of simultaneous estimation of F and x_t based on the latest available information is proposed. Real O-D data from the the Taipei rapid transit system is used to verify the presented model and solution method. Preliminary results are generally satisfactory, showing that in the unknown transition matrix case, significant estimates are also achieved.