Maximum likelihood estimation of inflation factors on error covariance matrices for ensemble Kalman filter assimilation

By Xiao Liang, Xiaogu Zheng, Shupeng Zhang, Guocan Wu, Yongjiu Dai, Yong Li. 2012

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An iterative ensemble Kalman smoother (2014, background): “Like other adaptive inflation schemes (Anderson, 2007; Miyoshi, 2011; Liang et al., 2012), the inflation of the prior is implicitly tuned so as to optimize a criterion, related to the likelihood of the innovations given their prior statistics.”
Expanding the validity of the ensemble Kalman filter without the intrinsic need for inflation (2015, methodology): “Other efficient adaptive inflation methods have been proposed by, e.g., Wang and Bishop (2003), Anderson (2007), Li et al. (2009), Zheng (2009), Brankart et al. (2010), Miyoshi (2011), Liang et al. (2012), and Ying and Zhang (2015) for broader uses including extrinsic model error.”
Enhanced Adaptive Inflation Algorithm for Ensemble Filters (2018, background): “The idea behind inflating the observation error variance is to compensate for a wrongly specified error distribution on the observations (Liang et al. 2012) and, in other scenarios, to limit the impact of theKalman update.”
Data assimilation in the geosciences: An overview of methods, issues, and perspectives (2017, unknown): “Hence, adaptive schemes have been developed to make the task more automatic (Anderson, 2007; Bocquet, 2011; Bocquet, Raanes, & Hannart, 2015; Bocquet & Sakov, 2012; Brankart, Cosme, Testut, Brasseur, & Verron, 2010; Li, Kalnay, & Miyoshi, 2009; Liang et al., 2012; Miyoshi, 2011; Wang & Bishop, 2003;”