Robustness and Computational Efficiency of Kalman Filter Estimator of Time-Dependent Origin–Destination Matrices

Abstract

Origin-Destination (OD) trip matrices, which describe the patterns of traffic behavior across the network, are the primary data input used in principal traffic models and therefore, a critical requirement in all advanced systems that are supported by Dynamic Traffic Assignment models. However, because OD matrices are not directly observable, the current practice consists of adjusting an initial or seed matrix from link flow counts which are provided by an existing layout of traffic counting stations. The availability of new traffic measurements provided by Information and Communication Technologies (ICT) applications allows more efficient algorithms, namely for the real-time estimation of OD matrices based on modified Kalman Filtering approaches exploiting the new data. The quality of the estimations depends on various factors, like the penetration of the ICT devices, the detection layout and the quality of the initial information. Concerning the feasibility of real-time applications, another key aspect is the computational performance of the proposed algorithms for urban networks of sensitive size. This paper presents the results of a set of computational experiments with a microscopic simulation of a network of the business district of Barcelona, which explore the sensitivity of the Kalman Filter estimates with respect to the values of the design factors, and its computational performance.

A Primal-Dual Algorithm for Link Dependent Origin Destination Matrix Estimation

“…Last, one could think about implementing time dependencies. This could be done by adding new relationships that would link successive estimations of the LODM or, alternatively, by using other methods: for example, a Kalman filter similarly to what have been done on traffic counts based ODM estimation [46], or also with supplementary data (e.g., Bluetooth [47] or other sensors [48]).…”

Towards a generic benchmarking platform for origin–destination flows estimation/updating algorithms: Design, demonstration and validation

“…Further, Sohn and Kim (2008) used cell-based trajectories as probe phones to estimate the average path choice proportions. Barceló et al (2010) proposed an efficient on-line approach based on linear Kalman filtering for linear structures, subsequently extended to general networks (Barceló et al, 2013), coping with congestion effects by the use of travel times provided by new ICT technologies. Integration of route flow data into the dynamic OD demand estimation problem was tackled by researchers in terms of either turning fractions (e.g.…”

Traffic Management for Smart Cities

“…However, although in general all these approaches have proven their robustness in terms of convergence to sound solutions, most of them have so cumbersome computational requirements that they are not applicable to support real-time decisions. Among the various factors determining the computational performance, the quality of the initial OD estimate proved to be critical [11]. A solution to the initialization problem could be to adjust OD matrices exploiting available traffic measurements and using a static off-line approach.…”

“…Since the approach uses the AVI travel time measurements from Bluetooth equipped vehicles, the non-linear approximations can be replaced by estimates from a sample of vehicles. Then no extra state variables for modeling travel times and traffic dynamics are needed, since sampled travel times are used to estimate discrete travel time distribution, see [11,12] for details.…”

“…A Kalman filter approach, with the recursive linear Kalman filter state space formulation [11,12], is adapted to exploit traffic counts collected by AVI sensors and conventional detection technologies, and travel times observed by the AVI sensors.…”