Error transfer analysis of normalized multichannel measurement

Abstract

In multichannel measurement, multiple signals affect the output result through the normalization process. It is difficult to analyze the error transfer, which represents the relation between the error of input and output, in this kind of measurement, especially in the normalization process. Thus, a new method of error transfer analysis is needed. Taking the primary spectrum pyrometry for example, this paper establishes a model for error transfer analysis in three-channel measurement by introducing the concept of solid angle. In the model, the error transfer is represented by the concept of error magnification, which is a dimensionless ratio of projection area of error sphere on the normalized plane to the cross section area of the error sphere. The error magnification can not be measured actually through experiment, but can be obtained from theoretical calculation. It is useful in the design of measurement system, especially the analysis of influence of different gain in different channel. The influence factors of the error magnification, including the absolute value and relation between them, are analyzed base on the model. The formula for analysis of two-channel and n-channel measurement is also derived from the three-channel model. Finally, some principles of operation and improvements in normalized multichannel measurement are proposed in order to reduce error.