Geometrical interpretation of Data Reconciliation and uncertainty reduction in Multi-Sensor systems

A data reconciliation and uncertainty reduction process, for multi-sensor systems such as power production plants, chemical processing plants, and many others, is considered. Methods of correcting original measurements to reduce their uncertainty, and to obtain more reliable information about the system, known as Data Validation and Reconciliation (DVR) or Process Data Reconciliation (PDR), have been developed in recent decades. These methods are present in literature as discussions on computer codes, statistical criteria, and details of specific industrial applications and implementations. This paper provides a mathematically accurate and intuitively understandable discussion on the scientific basis, benefits, limitations, and properties of the DVR/PDR tech-nology. This is achieved through geometrical interpretation of this technology in a multidimensional metric space with metric tensor defined by the set of the original measurements. The effect of various factors on the methods' output, are analyzed using graphical illustrations and analytical calculations.