A methodology for the online calibration of the speed–density relationship is formulated as a flexible state–space model. Applicable solution approaches are discussed and three of them–-the extended Kalman filter (EKF), the iterated EKF, and the unscented Kalman filter (UKF)–-are selected and presented in detail. An application of the methodology with freeway sensor data from two networks in Europe and the United States is presented. The improvement in the estimation and prediction of speeds due to online calibration (compared with the speeds obtained from the relationship calibrated offline) is demonstrated. EKF provided the most straightforward solution to this problem and, indeed, achieved considerable improvements in estimation and prediction accuracy. The benefits obtained from the use of the more computationally expensive iterated EKF algorithm are shown. An innovative solution technique (UKF) is also presented.
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