A generalization of optimal estimation for the retrieval of atmospheric vertical profiles

The optimal estimation method for the retrieval of atmospheric vertical profiles uses a priori information made of a profile and its covariance matrix. The underlying assumption is that the a priori profile has an averaging kernel matrix equal to the identity. The method is herewith generalized to the case that the a priori profile has a different averaging kernel matrix. The averaging kernel matrix of the a priori profile is properly taken into account in the cost function and a rigorous and more general solution for the optimal estimation method is derived.