The purpose of this paper is to provide a comprehensive presentation and interpretation of the Ensemble Kalman Filter (EnKF) and its numerical implementation. The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it. This paper reviews the important results from these studies and also presents new ideas and alternative interpretations which further explain the success of the EnKF. In addition to providing the theoretical framework needed for using the EnKF, there is also a focus on the algorithmic formulation and optimal numerical implementation. A program listing is given for some of the key subroutines. The paper also touches upon specific issues such as the use of nonlinear measurements, in situ profiles of temperature and salinity, and data which are available with high frequency in time. An ensemble based optimal interpolation (EnOI) scheme is presented as a cost-effective approach which may serve as an alternative to the EnKF in some applications. A fairly extensive discussion is devoted to the use of time correlated model errors and the estimation of model bias.

The Ensemble Kalman Filter: Theoretical formulation and practical implementation

Computer Aided Civil and Infrastructure Engineering

Transportation research. part c, emerging technologies

Deep neural networks (DNNs) have recently demonstrated the capability to predict traffic flow with big data. While existing DNN models can provide better performance than shallow models, it is still an open issue of making full use of spatial-temporal characteristics of the traffic flow to improve their performance. In addition, our understanding of them on traffic data remains limited. This paper proposes a DNN based traffic flow prediction model (DNN-BTF) to improve the prediction accuracy. The DNN-BTF model makes full use of weekly/daily periodicity and spatial-temporal characteristics of traffic flow. Inspired by recent work in machine learning, an attention based model was introduced that automatically learns to determine the importance of past traffic flow. The convolutional neural network was also used to mine the spatial features and the recurrent neural network to mine the temporal features of traffic flow. We also showed through visualization how DNN-BTF model understands traffic flow data and presents a challenge to conventional thinking about neural networks in the transportation field that neural networks is purely a “black-box” model. Data from open-access database PeMS was used to validate the proposed DNN-BTF model on a long-term horizon prediction task. Experimental results demonstrated that our method outperforms the state-of-the-art approaches.

A hybrid deep learning based traffic flow prediction method and its understanding

Traffic state estimation on highway: A comprehensive survey

Traffic management and traffic information are essential in urban areas, and require a good knowledge about both the current and the future traffic state. Both parametric and non-parametric traffic state prediction techniques have previously been developed, with different advantages and shortcomings. While non-parametric prediction has shown good results for predicting the traffic state during recurrent traffic conditions, parametric traffic state prediction can be used during non-recurring traffic conditions such as incidents and events. Hybrid approaches, combining the two prediction paradigms have previously been proposed by using non-parametric methods for predicting boundary conditions used in a parametric method. In this paper we instead combine parametric and non-parametric traffic state prediction techniques through assimilation in an Ensemble Kalman filter. As non-parametric prediction method a neural network method is adopted, and the parametric prediction is carried out using a cell transmission model with velocity as state. The results show that our hybrid approach can improve travel time prediction of journeys planned to commence 15 to 30 minutes into the future, using a prediction horizon of up to 50 minutes ahead in time to allow the journey to be completed.

A hybrid approach for short-term traffic state and travel time prediction on highways

Traffic management and traffic information are essential in urban areas and require reliable knowledge about the current and future traffic state. Parametric and nonparametric traffic state prediction techniques have previously been developed with different advantages and shortcomings. While nonparametric prediction has shown good results for predicting the traffic state during recurrent traffic conditions, parametric traffic state prediction can be used during nonrecurring traffic conditions, such as incidents and events. Hybrid approaches have previously been proposed; these approaches combine the two prediction paradigms by using nonparametric methods for predicting boundary conditions used in a parametric method. In this paper, parametric and nonparametric traffic state prediction techniques are instead combined through assimilation in an ensemble Kalman filter. For nonparametric prediction, a neural network method is adopted; the parametric prediction is carried out with a cell transmission model wit...

/pdf/hybrid-approach-for-short-term-traffic-state-and-travel-time-e34iqjre8u.pdf

Hybrid Approach for Short-Term Traffic State and Travel Time Prediction on Highways

Smart cities, participatory sensing as well as location data available in communication systems and social networks generates a vast amount of heterogeneous mobility data that can be used for traffic management . This chapter gives an overview of the different data sources and their characteristics and describes a framework for utilizing the various sources efficiently in the context of traffic management. Furthermore, different types of traffic models and algorithms are related to both the different data sources as well as some key functionalities of active traffic management, for example, short-term prediction and control.

/pdf/traffic-management-for-smart-cities-4m7i4o8msx.pdf

Traffic Management for Smart Cities

The need for accurate real-­time traffic information is growing in BLOCKIN

Mobile Millennium Stockholm

The velocity based cell transmission model (CTM-v) is a discrete time dynamical model that mimics the evolution of the traffic velocity field on highways. In this paper the CTM-v model is used together with an ensemble Kalman filter (EnKF) for the purpose of velocity sensor data assimilation. We present a calibration framework for the CTM-v and EnKF. The framework consists of two separate phases. The first phase is the calibration of the parameters of the fundamental diagram and the second phase is the calibration of demand and filter parameters. Results from the calibrated model are presented for a highway stretch north of Stockholm, Sweden.

Calibration Framework based on Bluetooth Sensors for Traffic State Estimation Using a Velocity based Cell Transmission Model

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