Abstract
In the past centuries, conventional levellings have been used to maintain the Dutch national height reference frame. Four primary levellings are carried out in the past century. Because the height benchmarks show significant motion, even within the time-span of one levelling campaign, their heights are better described by a (strict) kinematic model. We have developed Matlab-software in order to estimate the velocities of underground benchmarks, which form the backbone of the reference frame. The software performs a least squares parameter estimation, hypothesis testing and preprocessing. The amount of data, and more importantly, the rank defect may severely limit the possibilities of the model. Further research is needed to improve the model.
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References
Bruijne, A.J.T. de, F. Kenselaar and F. Kleijer (2001), ‘Kinematic Deformation Analysis of the First Order Benchmarks in The Netherlands’, presented at 10th FIG Int. Symp. on Deformation Measurements, Orange, California, 19–22 March 2001.
Dongarra, J.J., J.R. Bunch, C.B. Moler and G.W. Stewart (1979), UNPACK Users’ Guide, SIAM, Philadelphia.
Golub, G.H. and C.F. van Loan (1989), Matrix computations, 2nd edition, The Johns Hopkins University Press. Baltimore.
Heus, H. de, P. Joosten, M. Martens and H. Verhoef (1994), ‘Stability-Analysis as Part of the Strategy for the Analysis of the Groningen Gasfield Levellings’, presented at the Perelmutter Workshop on Dynamic deformation Models, 29 August - 1 September 1994, Haifa, Israel.
Koch, K.R. (1999), Parameter estimation and Hypothesis testing in Linear Models, 3rd edition, Springer-Verlag, Berlin.
Marel, H. van der (1988), On the “great circle reduction” in the data analysis for the astronomic satellite Hipparcos, PhD-thesis, Delft University of Technology.
Pissanetsky, S. (1984), Sparse matrix technology, Academic Press, London.
Sacher, M., J. Ihde, H. Schoh, D. Girrulat, R. Molendijk and K. Schmidt (2000), ‘Preliminary Results of Test Computations as a First Step, to a Kinematic Height Network’, presented at the EUREF Symposium Tromso, 22–24 June 2000, Norway.
Teunissen, P.J.G. (2000), Testing Theory, an introduction, Series on Mathematical Geodesy and Positioning, Delft University Press, Delft.
Verhoef, H.M.E. and H.M. de Heus (1995), ‘On the Estimation of Polynomial Breakpoints in the Subsidence of the Groningen Gasfield’, Survey Review, Vol. 33, 255, pp. 17–30.
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© 2002 Springer-Verlag Berlin Heidelberg
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Kleijer, F., Kenselaar, F., de Bruijne, A.J.T., Molendijk, R.E. (2002). Employing the Strict Kinematic Model for the Maintenance of a Height Reference Frame Based on Conventional Levellings. In: Drewes, H., Dodson, A.H., Fortes, L.P.S., Sánchez, L., Sandoval, P. (eds) Vertical Reference Systems. International Association of Geodesy Symposia, vol 124. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04683-8_23
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DOI: https://doi.org/10.1007/978-3-662-04683-8_23
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-07701-2
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