Joint Estimation of Model and Observation Error Covariance Matrices in Data Assimilation: a Review

Research paper by Pierre Tandeo, Pierre Ailliot, Marc Bocquet, Alberto Carrassi, Takemasa Miyoshi, Manuel Pulido, Yicun Zhen

Indexed on: 30 Jul '18Published on: 30 Jul '18Published in: arXiv - Statistics - Methodology


This paper is a review of a crucial topic in data assimilation: the joint estimation of model Q and observation R matrices. These covariances define the observational and model errors via additive Gaussian white noises in state-space models, the most common way of formulating data assimilation problems. They are crucial because they control the relative weights of the model forecasts and observations in reconstructing the state, and several methods have been proposed since the 90's for their estimation. Some of them are based on the moments of various innovations, including those in the observation space or lag-innovations. Alternatively, other methods use likelihood functions and maximum likelihood estimators or Bayesian approaches. This review aims at providing a comprehensive summary of the proposed methodologies and factually describing them as they appear in the literature. We also discuss (i) remaining challenges for the different estimation methods, (ii) some suggestions for possible improvements and combinations of the approaches and (iii) perspectives for future works, in particular numerical comparisons using toy-experiments and practical implementations in data assimilation systems.