Skip to main content
Log in

Generalised regression problems in metrology

  • Published:
Numerical Algorithms Aims and scope Submit manuscript

Abstract

This paper is concerned with generalised regression models in metrology. In experiments where much is known about the nature of the error in the measurement data, it is possible to build comprehensive mathematical models which lead to better estimates of the required parameter values. We indicate how efficient optimisation algorithms can be developed which exploit the structure of the corresponding regression problems and discuss applications in generalised distance regression and pressure metrology.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. P.T. Boggs, R.H. Byrd and R.B. Schnabel, A stable and efficient algorithm for nonlinear orthogonal distance regression, SIAM J. Sci. Statist. Comp. 8 (1987) 1052–1078.

    Article  Google Scholar 

  2. H.I. Britt and R.H. Luecke, The estimation of parameters in nonlinear, implicit models, Technometrics (1973) 233–247.

  3. M.G. Cox, The least squares solution of overdetermined linear equations having band or augmented band structure, IMA J. Numer. Anal. 1 (1981) 3–22.

    Google Scholar 

  4. M.G. Cox, The least-squares solution of linear equations with block-angular observation matrix, in:Advances in Reliable Numerical Computation, eds. M.G. Cox and S. Hammarling (Oxford University Press, 1989) pp. 227–240.

  5. M.G. Cox and H.M. Jones, An algorithm for least-squares circle fitting to data with specified uncertainty ellipses, IMA J. Numer. Anal. 9 (1989) 285–298.

    Google Scholar 

  6. M.G. Cox and H.M. Jones, A nonlinear least squares data fitting problem arising in microwave measurement, in:Algorithms for Approximation II, eds. J.C. Mason and M.G. Cox (Chapman Hall, London, 1990).

    Google Scholar 

  7. K.W.T. Elliott and P.B. Clapham, The accurate measurement of the volume ratios of vacuum vessels, Technical Report MOM 28, National Physical Laboratory, Teddington (1978).

    Google Scholar 

  8. A.B. Forbes, Fitting an ellipse to data, Technical Report DITC 95/87, National Physical Laboratory, Teddington (1987).

    Google Scholar 

  9. A.B. Forbes, Least squares best fit geometric elements, in:Algorithms for Approximation II, eds. J.C. Mason and M.G. Cox (Chapman Hall, London, 1990).

    Google Scholar 

  10. P.E. Gill, W. Murray and M.H. Wright,Practical Optimization (Academic Press, London, 1981).

    Google Scholar 

  11. G.H. Golub and C.F. Van Loan,Matrix Computations (North Oxford Academic, Oxford, 1983).

    Google Scholar 

  12. H.-P. Helfrich and D. Zwick, An improved Britt-Luecke algorithm for orthogonal distance regression, Numer. Algor. 5 (1993), this volume.

  13. K.V. Mardia, J.T. Kent and J.M. Bibby,Multivariate Analysis (Academic Press, London, 1979).

    Google Scholar 

  14. J.J. Moré, The Levenberg-Marquardt algorithm: implementation and theory, ed. G.A. Watson, in:Lecture Notes in Mathematics 630, (Springer, Berlin, 1977) pp. 105–116.

    Google Scholar 

  15. C.C. Paige, Fast numerically stable computations for generalized least squares problems, SIAM J. Numer. Anal. 16 (1979) 165–171.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Forbes, A.B. Generalised regression problems in metrology. Numer Algor 5, 523–533 (1993). https://doi.org/10.1007/BF02108667

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02108667

Keywords

Navigation