Unbiased ensemble square root filters

By D. Livings, Sarah L. Dance, N. Nichols. 2007

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Ensemble Kalman filtering without the intrinsic need for inflation (2011, background): “This property is important for the consistency and ultimately the stability and performance of the filter ( Wang et al. , 2004; Livings et al., 2008; Sakov and Oke , 2008).”
Estimating surface CO 2 fluxes from space-borne CO 2 dry air mole fraction observations using an ensemble Kalman Filter (2008, methodology): “However, approximations in EnKF approaches may lead to underestimation of the a posteriori uncertainties (Livings et al., 2008), in particular, when a reduced representation of the error covariance is used (see section 4.”
A Second-Order Exact Ensemble Square Root Filter for Nonlinear Data Assimilation (2015, methodology): “…2 for the ETKF, the transform matrix T of the NETF is not unique since an additional rotation of the ensemble in the space spanned by the ensemble members, ~T5TL , (24) does not change the mean and covariance of the ensemble as long asL is orthogonal and satisfiesL15 1 (Livings et al. 2008).”
Data assimilation in the geosciences: An overview of methods, issues, and perspectives (2017, background): “It was shown (Wang et al., 2004; Sakov and Oke, 2008b; Livings et al., 2008) that the symmetric square root preserves the zero mean in the updated perturbations.”