Error covariance estimation methods based on analysis residuals: theoretical foundation and convergence properties derived from simplified observation networks

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A Review of Innovation-Based Methods to Jointly Estimate Model and Observation Error Covariance Matrices in Ensemble Data Assimilation (2018, methodology): “When and how this method can result in accurate409 or inaccurate estimates, and convergence properties, have been studied in depth by Waller et al.410 (2016) and Ménard (2016).”
On the representation error in data assimilation (2018, unknown): “Concurrent iteration results in convergence in one step to a solution that may or may not be close to the true statistics (Ménard et al., 2009; Ménard, 2016).”