Tensorial calibration: II. Second‐order calibration

Abstract Tensorial calibration provides a useful approach to calibration in general. For calibration of instruments that produce two‐dimensional (second‐order) arrays of data per sample, tensoial concepts are as natural a way of solving the calibration problem as vectorial concepts are for the multivariate problem. Similarly, for third‐ and higher‐order data, the tensorial description of calibration is also useful. This paper introduces second‐order calibration from a tensorial point of view. Univariate, multivariate and bilinear approaches to calibration are presented. The generalized rank annihilation method (GRAM) is described from the tensorial perspective, and it is shown that GRAM is equivalent to finding a second‐order tensorial base that spans both tensors (calibration and unknown) with respective diagonal component matrices. GRAM uses a single calibration sample for multicomponent analysis even in the presence of interference. Second‐order bilinear calibration is extended to multiple calibration samples where the effect of collinearities is reduced.