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## Using non-diagonal R matrices with OMI

This feature was introduced with PDAF V2.3.

The default mode of PDAF-OMI is to use a diagonal observation error covariance matrix **R** and specifying the observation error variances, i.e. the diagonalof **R** only. This is in line with the common choice in data assimilation to assume that observation errors are uncorrelated.

However, there are also observation types with significant observation error correlations, which should be represented by a non-diagonal observation error covariance matrix. With PDAF V2.3 support for such nondiagonal **R** matrices was added to OMI.

PDAF-OMIs support for nondiagonal **R**-matrices consists in given the user access to the routines that perform operations involve **R**. This differs with the filter type, e.g. in LESTKF and LETKF a produce of some matrix with the inverse of **R** ha sto be computed, while in the traditional, perturbed observations, EnKF the matrix **R** has to be added to some other matrix. For the particle filter and the NETF the computation of the likelihood involves **R**.