State estimation in large networks require highly efficient data assimilation solutions. In this talk I discuss two traffic state estimation approaches that may be used to this end. The first is a localised version of the extended Kalman Filter (L-EKF), the second is a localised and deterministic version of the Ensemble Kalman filter (EnKF).
Both EKF and EnsKF (and all sequential Bayesian estimators for that matter) compute the expected value of the state vector alongside with the error co-variance matrix around this state estimate. The difference between EKF and EnsKF is that the former requires linearisation of the system model to predict and update the error covariance matrix, whereas the EnsKF approximates it through sequential sampling (i.e. by adding random observation errors). Although under many circumstances linearisation may be reasonable, around capacity it may lead to large errors, favouring an EnsKF approach, particularly because the latter is also much easier to implement. For both methods localisation increases computational complexity because it reduces (dramatically) the number of cross correlations between state vector components deemed relevant to compute the error co-variance matrix. Whereas the traditional EnsKF is a stochastic estimator, the deterministic scheme presented further addresses a number of numerical and computational problems affecting the former.
In the talk I briefly discuss these issues and show by means of a few examples the results of both approaches in terms of state estimation accuracy and computational performance.
Copyright. All Rights Reserved.