An algorithm for combining data sets having different frames of reference

B. P. Butler, A. B. Forbes

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1 Citation (Scopus)


The task of fitting a curve or surface to a number of related data sets is common in metrology. The data matching problem arises when sets of supplementary measurements are added to those of an underlying base set. Each supplementary set may have its own reference frame. This problem is formally equivalent to the data splicing problem in which no one set covers the entire region of interest. In either case, the presence of reference-frame transformation parameters means that least-squares fitting of a curve to the assembled data is generally a nonlinear problem. A linear version of this problem was treated in Anthony and Harris [1]. An algorithm is presented which exploits the inherent block structure of the problem, thereby reducing memory requirements and execution time. It employs the Gauss-Newton optimisation technique, returning both the fitting and reference-frame transformation parameters. The approach is quite general. Results are presented in the case of indentation analysis (for hardness testing, where the critical parameters are those of the fit). Applications also arise for which the transformation parameters are of primary interest; one such application is indicated.

Original languageEnglish
Pages (from-to)467-477
Number of pages11
JournalNumerical Algorithms
Issue number10
Publication statusPublished - Oct 1993
Externally publishedYes


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