Investigating the use of kalman filtering approaches for dynamic origin-destination trip table estimation

This paper studies the applicability of kalman filtering approaches for network wide traveler Origin Destination estimation from link traffic volumes. The paper evaluates the modeling assumptions of the Kalman filters and examines the implications of such assumptions. 1. Dynamic Origin Destination Tables Dynamic Origin-Destination (O-D) trip tables represent a time varying set of traffic demand patterns that occur for particular time periods between each Origin Destination pair. Dynamic O-D tables are an essential input for dynamic traffic assignment models and are useful for traclung time variable O-D patterns for on-line identification and control of traffic systems [6] . 1.1 Approaches for Estimating Dynamic O-D Trip Tables Till date two kinds of approaches for Dynamic 0D Estimation have been formulated: Parameter Optimization and Statistical approaches. Parameter optimization (Cremer and Keller (1987), [3], and Sherali et al [4]) formulations derive the O-D table by formulating objectives that minimize deviation between the actual traffic flow and that associated with the O-D table being derived. Statistical models may further be classified into statistical inference models (Maher [lo], Nihan and Davis [7] ) and kalman filtering models. 1.1.1 Kalman Filtering Approaches for O-D Estimation The difference (transition) equation) for Kalman Filter is of the form where Qk-,is the matrix of autoregressive coefficients, uk is a deterministic input, r , the control gain, A, the disturbance gain, and wk is the disturbance input. The measurement equation is given by (2) where nk is the error term. The filter computes the estimate of the state while minimizing the spread of the estimate error probability distribution function [5 ] . Assumptions used are: x k = $klXk-1 + ' k lUk-1 + ' k l W k l (l) xk = Hkxk ink The expected value of the initial state (x,) and its covariance ( Po ) are known: