Kalman filtering represents a powerful framework for solving data assimilation problems. Of interest here are the low-rank filters which are computationally efficient to solve large scale data assimilation problems. The low-rank filters are either based on factorization of the covariance matrix (RRSQRT filter), or approximation of statistics from a finite ensemble (ENKF). A new direction in filter implementation is the use of two filters next to each other of the same form or hybrid (POENKF). The factorization approach is based on the linear Kalman filter which can be extended towards nonlinear models. In this paper, the background, implementation and performance of some common used low-rank filters is discussed. Numerical results are presented.

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