Kalman filtering of large-scale geophysical flows by approximations based on Markov random field and wavelet

Large-scale extended Kalman filters for atmospheric and oceanic circulation models can readily be approximated using a wavelet transform or a Markov random field model. For a filtering problem where the unknown field of the state variables is highly correlated and the observations are relatively sparse, the wavelet-approximated filter seems more appropriate. For a problem in which the covariance matrix is non-singular and where a relatively large quantity of independent observations are processed, the MRF-approximated filter seems more appropriate.