Open AccessQuality quantifier of indirect measurements
Author(s) -
Simone Ceccherini,
B. Carli,
Piera Raspollini
Publication year - 2012
Publication title -
optics express
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.394
H-Index - 271
ISSN - 1094-4087
DOI - 10.1364/oe.20.005151
Subject(s) - quantifier (linguistics) , covariance , quality (philosophy) , jacobian matrix and determinant , mathematics , property (philosophy) , kernel (algebra) , distribution (mathematics) , statistics , computer science , mathematical analysis , physics , discrete mathematics , artificial intelligence , quantum mechanics , philosophy , epistemology
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.