Motivation
§Any data assimilation scheme requires accurate statistics for the observation and background errors. Unfortunately those statistics are not known and are usually tuned or adjusted by gut feeling.

§Ensemble Kalman filters need inflation (additive or multiplicative) of the background error covariance, but
 1) Tuning the inflation parameter is expensive especially if it is regionally dependent, and it may depend on time
 2) Miyoshi and Kalnay 2005 (MK) proposed a technique to objectively estimate the covariance inflation parameter.
 3) This method works, but only if the observation errors are known.

§ Here we introduce a method to simultaneously estimate observation errors and inflation.