Kalman Filter Applications for Traffic Management

An on­line calibration approach for dynamic traffic assignment systems has been developed. The approach is general and flexible and makes no assumptions on the type of the DTA system, the models or the data that it can handle. Therefore, it is applicable to a wide variety of tools including simulation­based and analytical, as well as microscopic and macroscopic models. The objective of the on­line calibration approach is to introduce a systematic procedure that will use the available data to steer the model parameters to values closer to the realized ones. The output of the on­line calibration is therefore a set of parameter values that --when used as input for traffic estimation and prediction-- minimizes the discrepancy between the simulated (estimated and predicted) and the observed traffic conditions. The scope of the on­line calibration is neither to duplicate nor to substitute for the off­line calibration process. Instead, the two processes are complementary and synergistic in nature. The on­line calibration problem is formulated as a state­space model. State­space models have been extensively studied and efficient algorithms have been developed, such as the Kalman Filter for linear models. Because of the non­linear nature of the on­line calibration formulation, modified Kalman Filter methodologies have been presented. The most straightforward extension is the Extended Kalman Filter (EKF), in which optimal quantities are approximated via first order Taylor series expansion (linearization) of the appropriate equations. The Limiting EKF is a variation of the EKF that eliminates the need to perform the most computationally intensive steps of the algorithm on­line. The use of the Limiting EKF provides dramatic improvements in terms of computational performance. The Unscented Kalman Filter (UKF) is an alternative filter that uses a deterministic sampling approach. The computational complexity of the UKF is of the same order as that of the EKF. Empirical results suggest that joint on­line calibration of demand and supply parameters can improve estimation and prediction accuracy of a DTA system. While the results obtained from this real network application are promising, they should be validated in further empirical studies. In particular, the scalability of the approach to larger, more complex networks needs to be investigated. The results also suggest that --in this application-- the EKF has more desirable properties than the UKF (which may be expected to have superior performance over the EKF), while the UKF seems to perform better in terms of speeds than in terms of counts. Other researchers have also encountered situations where the UKF does not outperform the EKF, e.g. LaViola, J. J., Jr. (2003) and van Rhijn et al. (2005). The Limiting EKF provides accuracy comparable to that of the best algorithm (EKF), while providing order(s) of magnitude improvement in computational performance. Furthermore, the LimEKF algorithm is that it requires a single function evaluation irrespective of the dimension of the state vector (while the computational complexity of the EKF and UKF algorithms increases proportionally with the state dimension). This property makes this an attractive algorithm for large­scale applications

Calibration of Traffic Simulation Models using SPSA

Εθνικό Μετσόβιο Πολυτεχνείο--Μεταπτυχιακή Εργασία. Διεπιστημονικό-Διατμηματικό Πρόγραμμα Μεταπτυχιακών Σπουδών (Δ.Π.Μ.Σ.) “Γεωπληροφορική

Improved Calibration Method for Dynamic Traffic Assignment Models

The calibration of dynamic traffic assignment (DTA) models involves the estimation of model parameters to best replicate real-world measurements. Good calibration is essential to estimate and predict accurately traffic states, which are crucial for traffic management applications to alleviate congestion. A widely used approach to calibrate simulation-based DTA models is the extended Kalman filter (EKF). The EKF assumes that the DTA model parameters are unconstrained, although they are in fact constrained; for instance, origin–destination (O-D) flows are nonnegative. This assumption is typically not problematic for small- and medium-scale networks in which the EKF has been successfully applied. However, in large-scale networks (which typically contain numbers of O-D pairs with small magnitudes of flow), the estimates may severely violate constraints. In consequence, simply truncating the infeasible estimates may result in the divergence of EKF, leading to extremely poor state estimations and predictions. To address this issue, a constrained EKF (CEKF) approach is presented; it imposes constraints on the posterior distribution of the state estimators to obtain the maximum a posteriori (MAP) estimates that are feasible. The MAP estimates are obtained with a heuristic followed by the coordinate descent method. The procedure determines the optimum and are computationally faster by 31.5% over coordinate descent and by 94.9% over the interior point method. Experiments on the Singapore expressway network indicated that the CEKF significantly improved model accuracy and outperformed the traditional EKF (up to 78.17%) and generalized least squares (up to 17.13%) approaches in state estimation and prediction

Calibration of Traffic Simulation Models using SPSA

Εθνικό Μετσόβιο Πολυτεχνείο--Μεταπτυχιακή Εργασία. Διεπιστημονικό-Διατμηματικό Πρόγραμμα Μεταπτυχιακών Σπουδών (Δ.Π.Μ.Σ.) “Γεωπληροφορική

A use of information and communication technologies in the framework of advanced management of transportation systems: dynamic OD matrix estimation

Origin-Destination (OD) trip matrices are the primary data input used in principal traffic and transit models, which describe the patterns of trips/passengers across the area of study. In this way, OD matrices become a critical requirement in Advanced Transport Management and/or Information Systems that are supported by Dynamic Assignment models. In the future, once combined dynamic traffic and transit assignment tools will be available to practitioners, the problem of estimating the time-dependent number of trips/passengers between transportation zones would be a critical aspect for real applications. However, because OD matrices are not directly observable, the current practice consists of adjusting an initial or seed matrix from link/segment counts which are provided by an existing layout of traffic counting stations or data gathering in the field (detection layout) for non-dynamic models. The typical approaches to time-dependent OD estimation have been based either on Kalman-Filtering or on bi-level mathematical programming approaches that can be considered in most cases as ad hoc heuristics. The advent of the new Information and Communication Technologies (ICT) makes available new types of real-time traffic and passenger data with higher quality and accuracy, allowing new modeling hypotheses which lead to more computationally efficient algorithms. This paper presents a Kalman Filtering approach that explicitly exploits data available from Bluetooth sensors to simplify an underlying space-state model, and describes the validation of the proposal through a set of simulation experiments, either on networks or corridors. Those involve car data provided by the detection of the electronic signature of on-board devices. Finally, an extension of the framework to the estimation of passenger matrices is addressed when data from passenger’s electronic signature devices are available.Peer ReviewedPostprint (author’s final draft

A dynamic estimation of passenger OD matrices based on space-state models

Dynamic OD passenger matrices must be taken into account when designing robust public transport systems. The adjustment of these matrices is examined using passenger counts provided by a space-state model formulation in a demand-variable peak-period. The Kalman filter approach also incorporates ICT data, based on the detection of the electronic signature of on-board devices, thus providing a rich source of data that can be used in space-state models to simplify its formulation. It reduces the dimension of the state vector and allows a linear mapping between state variables and measurements.Peer ReviewedPostprint (author’s final draft

An integrated method for short-term prediction of road traffic conditions for intelligent transportation systems applications

The paper deals with the short-term prediction of road traffic conditions within Intelligent Transportation Systems applications. First, the problem of traffic modeling and the potential of different traffic monitoring technologies are discussed. Then, an integrated method for short-term traffic prediction is presented, which integrates an Artificial Neural Network predictor that forecasts future states in standard conditions, an anomaly detection module that exploits floating car data to individuate possible occurrences of anomalous traffic conditions, and a macroscopic traffic model that predicts speeds and queue progressions in case of anomalies. Results of offline applications on a primary Italian motorway are presented

Towards Developing a Travel Time Forecasting Model for Location-Based Services: a Review

Travel time forecasting models have been studied intensively as a subject of Intelligent Transportation Systems (ITS), particularly in the topics of advanced traffic management systems (ATMS), advanced traveler information systems (ATIS), and commercial vehicle operations (CVO). While the concept of travel time forecasting is relatively simple, it involves a notably complicated task of implementing even a simple model. Thus, existing forecasting models are diverse in their original formulations, including mathematical optimizations, computer simulations, statistics, and artificial intelligence. A comprehensive literature review, therefore, would assist in formulating a more reliable travel time forecasting model. On the other hand, geographic information systems (GIS) technologies primarily provide the capability of spatial and network database management, as well as technology management. Thus, GIS could support travel time forecasting in various ways by providing useful functions to both the managers in transportation management and information centers (TMICs) and the external users. Thus, in developing a travel time forecasting model, GIS could play important roles in the management of real-time and historical traffic data, the integration of multiple subsystems, and the assistance of information management. The purpose of this paper is to review various models and technologies that have been used for developing a travel time forecasting model with geographic information systems (GIS) technologies. Reviewed forecasting models in this paper include historical profile approaches, time series models, nonparametric regression models, traffic simulations, dynamic traffic assignment models, and neural networks. The potential roles and functions of GIS in travel time forecasting are also discussed.

Estimation of origin-destination matrix from traffic counts: the state of the art

The estimation of up-to-date origin-destination matrix (ODM) from an obsolete trip data, using current available information is essential in transportation planning, traffic management and operations. Researchers from last 2 decades have explored various methods of estimating ODM using traffic count data. There are two categories of ODM; static and dynamic ODM. This paper presents studies on both the issues of static and dynamic ODM estimation, the reliability measures of the estimated matrix and also the issue of determining the set of traffic link count stations required to acquire maximum information to estimate a reliable matrix