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The Compressed State Kalman Filter For Nonlinear State Estimation: Application To Large-Scale Reservoir Monitoring, J Y. Li, Amalia Kokkinaki, H Ghorbanidehno, E F. Darve, P K. Kitanidis

Environmental Science

Reservoir monitoring aims to provide snapshots of reservoir conditions and their uncertainties to assist operation management and risk analysis. These snapshots may contain millions of state variables, e.g., pressures and saturations, which can be estimated by assimilating data in real time using the Kalman filter (KF). However, the KF has a computational cost that scales quadratically with the number of unknowns, m, due to the cost of computing and storing the covariance and Jacobian matrices, along with their products. The compressed state Kalman filter (CSKF) adapts the KF for solving large-scale monitoring problems. The CSKF uses N preselected orthogonal …