T. Schreiter

Localized Extended Kalman Filter for Scalable Real-Time Traffic State Estimation

Current or historic traffic states are essential input to advanced traveler information, dynamic traffic management, and model predictive control systems. As traffic states are usually not perfectly measured and are everywhere, they need to be estimated from local and noisy sensor data. One of the most widely applied estimation methods is the Lighthill-Whitham and Richards (LWR) model with an extended Kalman filter (EKF). A large disadvantage of the EKF is that it is too slow to perform in real time on large networks. To overcome this problem, the novel localized EKF (L-EKF) is proposed in this paper. The logic of the traffic network is used to correct only the state in the vicinity of a detector. The L-EKF does not use all information available to correct the state of the network; the resulting accuracy is equal, however, if the radius of the local filters is sufficiently large. In two experiments, it is shown that the L-EKF is much faster than the traditional Global EKF (G-EKF), that it scales much better with the network size, and that it leads to estimates with nearly the same accuracy as the G-EKF and when the spacing between detectors is varied somewhere between 0.7 and 5.1 km. Compared with the G-EKF, the L-EKF is a highly scalable solution to the state estimation problem.

Freeway traffic state estimation using extended Kalman filter for first-order traffic model in Lagrangian coordinates

Freeway traffic state estimation is one of the central components in real-time traffic management and information applications. Recent studies show that the classic kinematic wave model can be formulated and solved more efficiently and accurately in Lagrangian (vehicle number-time) coordinates. This paper investigates the opportunities of the Lagrangian form for state estimation. The main advantage for state estimation is that in Lagrangian coordinates, the numerical solution scheme is reduced to an upwind scheme. We propose a new model-based extended Kalman filter (EKF) state estimator where the discretized Lagrangian model is used as the model equation. This state estimator is applied to freeway traffic state estimation and validated using synthetic data. Different filter design specifications with respect to measurement aspects are considered. The achieved results are very promising for subsequent studies.

Two fast implementations of the Adaptive Smoothing Method used in highway traffic state estimation

Freeway traffic state estimation is crucial for dynamic traffic management (DTM), Advanced Traveler Information Systems (ATIS) and highway performance analyses. Raw data collected by dual-loop detectors or GPS devices provide information about flow and speed at points in space and time. However, these observations are noisy and incomplete. The Adaptive Smoothing Method (ASM) estimates the traffic state between the observation points and reduces the noise inherent to observations. Current implementations of the ASM apply its model in a straight-forward manner, which leads to high computation times. In this paper, two new implementations are developed that drastically reduce the computation time while preserving the estimation quality. In the first implementation, the ASM is discretized to apply the cross-correlation. This is based on matrix operations, which are efficiently implemented and fast in execution. In the second implementation, the ASM is reformulated to apply the Fast Fourier Transform (FFT). The FFT, too, is based on fast matrix operations. These two new implementations are sequential programs, containing no loops. Experiments with a setup used in practical applications and real data show computation times of just a few seconds. These are computation time improvements of two orders of magnitude. The rapid computation of the traffic state makes the ASM with the proposed implementations applicable for real-time applications.

Multi-class ramp metering: Concepts and initial results

Ramp Metering is often applied in Dynamic Traffic Management (DTM) to control the inflow onto freeways. Although traffic usually consists of different vehicle classes such as cars and trucks, these conventional ramp meter installations operate on all classes equally, thereby disregarding the traffic composition. This paper introduces a multi-class ramp meter (MCRM) which controls the traffic vehicle-class specifically. It regulates the inflow to ascertain a specified inflow composition. In this contribution, the control algorithm of multi-class ramp metering is presented. Furthermore, the effects on travel time, queue length and total delay are outlined.

Policy-Based, Service Level-Oriented Route Guidance in Road Networks

The realization of traffic management on a network level is not only theoretically complex, but also practically challenging because the traffic management policy of the road authorities must be taken into account. In the Netherlands, this policy harmonizes the interests of involved stakeholders by means of a common vision on the functioning of the network, expressed in road priorities and the corresponding target service levels. As a result, network states that reflect the policys objectives in a systematic and comprehensible way must be realized. This paper presents a predictive route guidance approach that is able to operationalize the formulated policy. This approach degrades and restores target service levels of routes according to their difference in priority, with respect to the network performance. The control approach consists of a finite state machine that determines target service levels according to predicted traffic conditions. These target service levels are used as setpoints in a feedback controller, and the result is a corresponding output signal of a variable message sign. By means of a test case, the finite state machine is compared with a model predictive route guidance controller (that realizes system optimal conditions) and with a user equilibrium feedback controller (that realizes user optimal conditions). Results showed that the finite state machine was able to prevent or limit the effects of phenomena that caused decreased network performance in a comprehensible and efficient way while also accounting for the interests of the road users.

Vehicle-class Specific Route-guidance of Freeway Traffic by Model-predictive Control

Few active traffic management measures proposed in the past considered the distinction of different vehicle classes. Examples of measures specific to vehicle class are truck lanes and high-occupancy toll lanes. It is proposed that the distinction of different vehicle classes, with different flow characteristics and societal and economic functions, can contribute to the effectiveness of traffic management measures. This study developed a multiclass controller that rerouted the traffic class specifically. Vehicle class–specific properties such as vehicle length and value of time were used in a model-predictive control approach to minimize the total time spent in the network by vehicles and the corresponding economic costs. By means of a simple test case with synthetic data, it was shown that a multiclass controller outperformed a single-class controller and that the multiclass control signals were sensitive to the value of time and the capacity of the network.

Fast traffic state estimation with the localized Extended Kalman Filter

Traffic state estimation is important input to traffic information and traffic management systems. A wide variety of traffic state estimation methods exist, either data-driven or model-driven. In this paper a model-driven approach is used: the LWR model solved by the Godunov scheme. The most widely applied method to combine this model with real-time data is the Extended Kalman Filter (EKF). A large disadvantage of the EKF is that it is too slow to perform in real-time on large networks. In this paper the novel Localized EKF (L-EKF) is proposed that sequentially makes many local corrections instead of one large global correction. The L-EKF does not use all information available to correct the state of the network, but in an experiment it is shown that the resulting loss of accuracy is negligible in case the radius of the local filters is taken sufficiently large. The L-EKF hence is a highly scalable solution to the state estimation problem that results in equally accurate state estimates.

Modeling monetary costs of multi-class traffic flow - Application to the dynamic management of truck lanes

Traffic is composed of different vehicle classes, each characterized by the vehicle length, the value of time (VOT) and other class-specific properties. Multi-class traffic flow models aim to capture these class-specific differences. In this paper, a multi-class model is appended with a monetary cost framework accounting for the value of time of each vehicle class, thereby enabling the computation of the total network costs. Subsequently, the framework is analytically applied to show the conditions under which it is justified to prioritize certain traffic classes in order to maximize the monetary flow (which is equivalent to minimizing the total monetary network costs). An illustrative example is given in which the framework is used to find the conditions (bottleneck capacity, traffic demand, pce, VOT) under which activating a dedicated lane for trucks is beneficial.