Low rank unscented Kalman filter for freeway traffic estimation problems

摘要

Data assimilation techniques are a process of using measurements combined withmodel predictions to (optimally) estimate the value of a certain set of variables. Thesetechniques belong to a group of model-based estimation approach. In traffic science, theKalman filter and its family, namely extended Kalman filter (EKF), have been widely appliedto traffic state estimation problems. Basically, the EKF is successful in terms of computationand provides some reasonably accurate results. However, traffic systems are generally sononlinear that the linearization used in the EKF is not always straightforward. To avoid suchlinearization, another family of Kalman filter, the unscented Kalman filter (UKF), has beendesigned to account for the nonlinear system in which a set of deterministic sample points arechosen to capture the initial probability distribution. These sample points are then propagatedthrough the nonlinear system and the probability density function of the actual state isapproximated by the ensemble of the estimates. In the UKF, the number of sample points isdetermined by the dimension of the states to be estimated so that it will become rathercomputationally expensive when the size of traffic networks is increased. To this end, thispaper is dedicated to the approximation of the UKF in which the required sample points arereduced. Numerical experiments were carried out to assess the relevance of the proposedapproach with real traffic data and comparisons with the UKF regarding the level of accuracyand computational time were made.