The Kalman Filter is used in a number of linear estimation and machine learning applications for estimating parameters in traffic control. These include estimating the state of a linear dynamic system and its parameters. In case that all variables are measurable, the Kalman filter is linear. In more practical case, when there are un-measurable variables, it is nonlinear. The model is non-linear since it contains non-linear relation between queue length and occupation, and unknown parameters. Hence, the standard Kalman filter is not suitable and therefore EKF (extended KF) has to be used and its innovations (DD2 filter) for estimation of the traffic model. Three filters are presented and compared for the nonlinear state estimation of the state-space model for traffic control. The EKF algorithm is simple but it can become unstable. This is not acceptable and two more sophisticated filters were tested. First, the UKF (Unscented Kalman Filter) is based on sampling, and its computational demand is comparable to that of EKF. Second, the DD2 filter which replaces the derivation by divided differences. (The DD2 filter is based on second-order Taylor approximations.) It appears that neither UKF nor DD2 can be directly applied to the problem. Further modifications of these filters are needed.
Application of the Kalman filter in traffic
Anwendung des Kalman-Filters in der Verkehrslenkung
2005
5 Seiten, 2 Bilder, 10 Quellen
Conference paper
Storage medium
English
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