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

Pavement Performance Evaluation Using Connected Vehicles

Roads deteriorate at different rates from weathering and use. Hence, transportation agencies must assess the ride quality of a facility regularly to determine its maintenance needs. Existing models to characterize ride quality produce the International Roughness Index (IRI), the prevailing summary of roughness. Nearly all state agencies use Inertial Profilers to produce the IRI. Such heavily instrumented vehicles require trained personnel for their operation and data interpretation. Resource constraints prevent the scaling of these existing methods beyond 4% of the network. This dissertation developed an alternative method to characterize ride quality that uses regular passenger vehicles. Smartphones or connected vehicles provide the onboard sensor data needed to enable the new technique. The new method provides a single index summary of ride quality for all paved and unpaved roads. The new index is directly proportional to the IRI. A new transform integrates sensor data streams from connected vehicles to produce a linear energy density representation of roughness. The ensemble average of indices from different speed ranges converges to a repeatable characterization of roughness. The currently used IRI is undefined at speeds other than 80 km/h. This constraint mischaracterizes roughness experienced at other speeds. The newly proposed transform integrates the average roughness indices from all speed ranges to produce a speed-independent characterization of ride quality. This property avoids spatial wavelength bias, which is a critical deficiency of the IRI. The new method leverages the emergence of connected vehicles to provide continuous characterizations of ride quality for the entire roadway network. This dissertation derived precision bounds of deterioration forecasting for models that could utilize the new index. The results demonstrated continuous performance improvements with additional vehicle participation. With practical traversal volumes, the achievable precision of forecast is within a few days. This work also quantified capabilities of the new transform to localize roadway anomalies that could pose travel hazards. The methods included derivations of the best sensor settings to achieve the desired performances. Several case studies validated the findings. These new techniques have the potential to save agencies millions of dollars annually by enabling predictive maintenance practices for all roadways, worldwide.Mountain Plains Consortium (MPC

Applications

Volume 3 describes how resource-aware machine learning methods and techniques are used to successfully solve real-world problems. The book provides numerous specific application examples: in health and medicine for risk modelling, diagnosis, and treatment selection for diseases in electronics, steel production and milling for quality control during manufacturing processes in traffic, logistics for smart cities and for mobile communications

Doctor of Philosophy

dissertationThis dissertation aims to develop an innovative and improved paradigm for real-time large-scale traffic system estimation and mobility optimization. To fully utilize heterogeneous data sources in a complex spatial environment, this dissertation proposes an integrated and unified estimation-optimization framework capable of interpreting different types of traffic measurements into various decision-making processes. With a particular emphasis on the end-to-end travel time prediction problem, this dissertation proposes an information-theoretic sensor location model that aims to maximize information gains from a set of point, point-to-point and probe sensors in a traffic network. After thoroughly examining a number of possible measures of information gain, this dissertation selects a path travel time prediction uncertainty criterion to construct a joint sensor location and travel time estimation/prediction framework. To better measure the quality of service for ransportation systems, this dissertation investigates the path travel time reliability from two perspectives: variability and robustness. Based on calibrated travel disutility functions, the path travel time variability in this research is represented by its standard deviation in addition to the mean travel time. To handle the nonlinear and nonadditive cost functions introduced by the quadratic forms of the standard deviation term, a novel Lagrangian substitution approach is introduced to estimate the lower bound of the most reliable path solution through solving a sequence of standard shortest path problems. To recognize the asymmetrical and heavy-tailed travel time distributions, this dissertation proposes Lagrangian relaxation based iterative search algorithms for finding the absolute and percentile robust shortest paths. Moreover, this research develops a sampling-based method to dynamically construct a proxy objective function in terms of travel time observations from multiple days. Comprehensive numerical experiment results with real-world travel time measurements show that 10-20 iterations of standard shortest path algorithms for the reformulated models can offer a very small relative duality gap of about 2-6%, for both reliability measure models. This broadly-defined research has successfully addressed a number of theoretically challenging and practically important issues for building the next-generation Advanced Traveler Information Systems, and is expected to offer a rich foundation beneficial to the model and algorithmic development of sensor network design, traffic forecasting and personalized navigation