Comparison of the Ensemble Kalman filter with the Unscented Kalman filter : application to the construction of a road embankment

EnKF was designed to resolve two major problems related to the use of EKF. The first problem relates to the use of an approximate closure scheme in the EKF (first order Taylor expansion). The second problem relates to the huge computational requirements associated with the storage and forward integration of the error covariance matrix P. For further details the reader is referred to the references. In the Ensemble Kalman filter, an ensemble of possible state vectors, which are randomly generated using a Monte Carlo approach, represents the statistical properties of the state vector. The algorithm does not require a tangent linear model, which is required for the EKF, and is very easy to implement.