Skip to main content
SpringerLink
Log in

Generalyzed variance-covariance propagation law formulae and application to explicit least-squares adjustments

  • Published:
Bulletin géodésique Aims and scope Submit manuscript

Abstract

Standard formulae overlook the contribution of a number of terms in the derivation of variance-covariance matrices for parameters in nonlinear least squares adjustment. In a large class of nonlinear mathematical models, these terms can contribute to an important error in the estimation of parameter variances. Improved formulae are derived. A numerical example is given and the use of our improved formula in the case of least-squares adjustment in the explicit case (L=F(X)) is fully documented.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • M.J. BOX. Bias in Non-Linear Estimation (with Discussion). J.R. Stat. Soc. B32, pp. 171–201, 1971.

    Google Scholar 

  • A. GRAHAM: Kronecker Products and Matrix Calculus with Applications. Chichester: Ellis Horwood, 1981.

    Google Scholar 

  • J.R. MAGNUS and H. NEUDECKER. The Commutation Matrix: Some Properties and Applications. Ann. Stat.,7, No. 2, pp. 381–394, 1979.

    Article  Google Scholar 

  • A.J. POPE: Two Approaches to Nonlinear Least Squares Adjustments. Can. Surv.,28, No. 5, pp. 663–669, 1974.

    Google Scholar 

  • A.J. POPE: Some Pitfalls to be Avoided in the Iterative Adjustment of Nonlinear problems. Proc. 38th an. meet. Am. Soc. Phot., March, 1972.

  • C.R. RAO: Linear Statistical Inference and Its Applications. 2nd ed. John Wiley & Sons, Inc., New York, 1973.

    Google Scholar 

  • B. SCHAFFRIN: A note on linear prediction within a Gauss-Markoff model linearized with respect to a random approximation. Proc. First Tampere Sem. Linear Models, Dep. Math., Un. Tampere, Finland, 1983.

  • H.J. SCHECK and P. MAIER: Nichtlineare Normal Gleichungen zur Bestimmung der Unbekannten und deren Kovarianzmatrix. ZfV,101, pp. 149–159, 1976.

    Google Scholar 

  • P.J.G. TEUNISSEN: The Geometry of Geodetic Inverse Linear Mapping and Non-Linear Adjustment. Neth. Geod. Com., New Series, Vol. 8, No. 1, 1985a.

  • P.J.G. TEUNISSEN. A note on the use of Gauss’Formulas in nonlinear geodesic adjustment. Stat. & Decisions, Symp. No. 2, pp. 455–466, R. Oldenburg Verlag, München, 1985b.

    Google Scholar 

  • P. VANÍČEK and E.J. KRAKIWSKY: Geodesy: the Concepts, North-Holland Pub. Co., New York, 1982.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Geodetic Sciences and Remote Sensing Pavillon Casault, Laval University, G1K 7P4, Ste-Foy, Qc, Canada

    Luc M. A. Jeudy

Authors
  1. Luc M. A. Jeudy
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jeudy, L.M.A. Generalyzed variance-covariance propagation law formulae and application to explicit least-squares adjustments. Bull. Geodesique 62, 113–124 (1988). https://doi.org/10.1007/BF02519220

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02519220

Keywords

Search

Navigation