Summary
One of the classical procedures for geodetic network densification consists in a free net adjustment, followed by a so-called “Helmert transformation” with respect to the fiducial point set which is kept unchanged. Here we show that this approach is not optimal in terms of the Mean-Squared-Error (MSE) risk, and present a direct derivation, based on the least-squares principle, of the optimal densification solution with the “reproducing property”.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aduol, F. W. O.: A static-dynamic model for densification of geodetic networks, AVN-Intl. Edition 10 (1993), 20–36
Buiten, H. J.: Junction of nets by collocation, Manus. Geo-daet. 3 (1978), 253–297
Grafarend, E., Knickmeyer, E., Schaffrin, B.: Geodetic datum transformations (in German). ZfV 107 (1982), 15–25
Grafarend, E., Schaffrin, B.: Unbiased free net adjustment, Survey Review 22 (1974), 200–218
Grafarend, E., Schaffrin, B.: Equivalence of estimable quantities and invariants in geodetic networks, ZfV 101 (1976), 485–491
Grafarend, E., Schaffrin B.: From the static to the dynamic treatment of geodetic networks (in German), ZfV 113 (1988), 79–103
Koch, K. R.: The choice of the datum of a trigonometric network for the determination of new points (in German), ZfV 108 (1983), 104–111
Lichten, S. M., Bertiger, W. L, Lindqwister, Ulf J.: The effect of fiducial network strategy on high-accuracy orbit and baseline determination; In: Stein, W. L./Kumar, M. (eds), Proc. of the 5th Intl. Geodetic Symp. on Satellite Positioning, Las Cruces, NM, USA, 1989, Vol. I, pp. 516–525
Schaffrin, B.: On the use of prior information in free networks (in German); In: Rinner, K. et al. (eds), Ingenieur-Vermessung ‘84, Dümmler: Bonn, B6/1–15, 1984
Schaffrin, B.: Fiducial versus fixed points in the GPS network approach; In: Stein, W. L./Kumar, M. (eds.), Proc. of the 5th. Intl. Geodetic Symp. on Satellite Positioning, Las Cruces, NM, USA, 1989, Vol. I. pp. 500–511
Schaffrin, B.: On suboptimal geodetic network fusion, Poster paper, IAG General Meeting, Rio de Janeiro, Brazil, Sept. 1997
Schaffrin, B., Cothren, J.: Towards optimizing hierarchial data revisions, Proc. of the Intl. Symp. on GIS: Between Visions and Applications, Stuttgart, Germany, Sept. 1998, pp. 515–521
Tamim, N., Schaffrin, B.: A methodology to create a digital cadastral overlay..., Surv. & Land Info. Syst. 55 (1995), 3–12.
Xu, P.: Personal communication, DPRI, Univ. of Kyoto, Sept. 1999
Editor information
Editors and Affiliations
Additional information
Dedicated to Erik Grafarend at his 60th birthday
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Schaffrin, B. (2003). Reproducing Estimators via Least-Squares: An Optimal Alternative to the Helmert Transformation. In: Grafarend, E.W., Krumm, F.W., Schwarze, V.S. (eds) Geodesy-The Challenge of the 3rd Millennium. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-05296-9_40
Download citation
DOI: https://doi.org/10.1007/978-3-662-05296-9_40
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-07733-3
Online ISBN: 978-3-662-05296-9
eBook Packages: Springer Book Archive