Tensorial Calibration. 2. Second Order Tensorial Calibration.
Abstract
Tensorial calibration provides a useful approach to calibration in general. For calibration of instruments that produce two dimensional (second order) data arrays of data per sample, tensorial concepts are a natural way of solving the calibration problems as vectorial concepts are for multivariate problems. 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 of multicomponent analysis even in the presence of interferences. Second order bilinear calibration is extended to multiple calibration samples, where the effect of collinearities is reduced.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 12, 1987
- Accession Number
- ADA186614
Entities
People
- Bruce R. Kowalski
- Eugenio Sanchez
Organizations
- University of Washington