Quality quantifier of indirect measurements

A quality quantifier, referred to as measurement quality
quantifier (MQQ), is proposed for indirect measurements. It satisfies the
property that the MQQ of the data fusion of two or more independent
measurements is the sum of the MQQs of the individual measurements and
can also be determined in absolute terms for ill-posed problems. It is
calculated from the covariance and Jacobian matrices of the observations,
but the same result is also obtained using the covariance and averaging
kernel matrices of the retrieved quantities. In the case of measurements of a
continuous distribution a quantifier that provides the information
distribution can be derived from the MQQ. The proposed quantifiers are
herewith used for the quality assessment of atmospheric ozone
measurements performed by IASI and MIPAS instruments.