Extended Kalman Filters, Least Squares Methods, and Successive Linear Estimator for Inverse Problems in Groundwater Flow

We formulate the problem of estimating hydraulic conductivity from measured hydraulic head data in groundwater flow within the unified framework of parameter estimation using the extended Kalman filter (EKF) and least-squares optimization. We first formulate the EKF and its variants as problems of least-squares optimization. We then show that the successive linear estimator can be interpreted as a variant of the EKF, with its initial estimate obtained through co-Kriging. Furthermore, by showing that the EKF is equivalent to a one-step Newton iteration for solving a least-squares problem, we reformulate the hydraulic conductivity estimation problem as an associated least-squares optimization problem. Finally, we present an algorithm for estimating hydraulic conductivity from unsaturated soil data.