The Extended and Ensemble Kalman Filters

In this chapterwe describe the Extended Kalman Filter (ExKF) 1 and the Ensemble Kalman Filter (EnKF). The ExKF approximates the predictive covariance by linearization, while the EnKF approximates it by the empirical covariance of a collection of particles. The ExKF is a provably accurate approximation of the filtering distribution if the dynamics are approximately linear and small noise is present in both signal and data, in which case the filtering distribution is well approximated by a Gaussian.