Heuristics and H-optimum Estimators in a Model with Type-I Constraints

  • Jaroslav Marek
  • Jana Heckenbergerova
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 303)


The aim in linear statistical models is to determine an estimator of the unknown parameters on the basis of the observation vector. One possible approach used mainly in geodetic measurements is known as \(\mathbf H\)-optimum estimator.

This paper deals with problem of connecting measurements where boundaries of estimators dispersion are previously known. The \(\mathbf H\)- optimum estimators seem to be appropriate for reducing the influence of B-type metrological uncertainty on the estimator in connecting measurement. However in this case, general \(\mathbf H\)-optimum estimators do not solve the problem of bounded dispersion completely.

Heuristic methods such as algorithm complex method help us to extend \(\mathbf H\)-optimum estimator theory so given dispersion boundaries could be satisfied. Presented paper describes standard theory of \(\mathbf H\)-optimum estimators and its extension with heuristics utilization. Finally, qualities of extended \(\mathbf H\)-optimum estimator are shown by solving illustration example.


Algorithm complex method linear statistical model \(\mathbf H\)-optimum estimators BLUE uncertainty of types A and B covariance matrix problem of bounds for dispersion of estimators 


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  1. 1.
    Rao, C.R., Mitra, S.K.: Generalized Inverse of Matrices and Its Applications. John Wiley & Sons, New York (1971)MATHGoogle Scholar
  2. 2.
    Rao, C.R.: Linear Statistical Inference and Its Applications, 2nd edn. J. Wiley, New York (1973)CrossRefMATHGoogle Scholar
  3. 3.
    Marek, J.: Estimation in connecting measurements. Acta Universitas Palackianae, Fac. Rer. Nat., Mathematica 42, 69–86 (2003)MATHMathSciNetGoogle Scholar
  4. 4.
    Kubáček, L.: Two stage regression models with constraints. Math. Slovaca 43, 643–658 (1993)MATHMathSciNetGoogle Scholar
  5. 5.
    Korbašová, M., Marek, J.: Connecting Measurements in Surveying and its Problems. In: Proceedings of INGEO 2004 and FIG Regional Central and Eastern European Conference on Engineering Surveying, Bratislava, Slovakia (2004)Google Scholar
  6. 6.
    Rao, S.S.: Engineering optimization. Theory and Practise. John Wiley & Sons, New York (1996)Google Scholar
  7. 7.
    Nelder, J.A., Mead, R.: A simplex method for function minimization. Computer Journal 7, 308–313 (1965)CrossRefMATHGoogle Scholar
  8. 8.
    Box, M.J.: A new method of constrained optimization and a comparison with other methods. Computer Journal 1, 42–52 (1965)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Department of Mathematics and Physics, Faculty of Electrical Engineering and InformaticsUniversity of PardubicePardubiceCzech Republic

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