A fast Kalman filter for time-lapse electrical resistivity tomography

We present a reduced complexity algorithm for time-lapse Electrical Resistivity Tomography (ERT) based on an extended Kalman filter. The key idea of the fast algorithm is an efficient representation of state covariance matrix at each step as a weighted combination of the system noise covariance matrix and a low-rank perturbation term. We propose an efficient algorithm for updating the weights and the basis of the low-rank perturbation. The overall computational cost at each iteration is O(Nn_m) and storage cost O(N), where N is the number of grid points, and n_m is the number of measurements. The performance of this algorithm is demonstrated on a challenging application of monitoring the CO₂ plume using synthetic ERT data.