Abstract The calibration of measuring instruments requires the calculation of inner and outer data errors. We use interval twins (twice intervals) to describe the data estimations. The linear regression problem uses inner estimates of the data to obtain more accurate estimates. On the one hand, inner estimates can give an empty set as a result, on the other hand, using only outer ones leads to huge solution sets. In such cases, using a combination of inner and outer evaluations is convenient. This paper discusses a solution of a Twin System of Linear Algebraic Equations and its application in the calibration process of Nuclear Fusion and Plasma Physics LIDAR-based data collection and analysis in nuclear fusion. Two algorithms for solving these systems are presented here: the first method replaces inner estimates with outer ones, and the second method includes additional intervals. The operation of the algorithms is demonstrated using examples with generated data. In addition, a histogram shows the number of unresolvable systems, with the data taken from the PSI DRS4 fast analog memory chip.
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