COMPARISON OF KALMAN FILTER ESTIMATION APPROACHES IN THE FIELD OF GEOMECHANICS

www.eme.okayama-u.ac.jp Key Words: Kalman Filter, Inverse Modelling, Parameter Estimation The Extended Kalman Filter (EKF) has been used in the field of geomechanics standard for nonlinear state space estimation (Murakami, 1991). However a couple of alternative approaches have emerged over the last few years, namely the Ensemble Kalman filter (EnKF) and the Unscented Kalman filter (UKF). Evensen introduced the EnKF in 1994 and the theoretical formulations as well as an overview of several applications are described in Evensen (2003). The 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, and the other one 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 propertie