Abstract
Existing position information in a network can be integrated with the densification solution in two ways: One way is to obtain a solution of the densification network followed by a merger of this and all other solutions or vice versa. Alternatively, the existing solutions (not used as weighted constraints) can be taken to be pseudo-observations in a simultaneous adjustment with the “new” observations. In both cases, all existing solutions must first be transformed to the coordinate system of the densified network and be statistically compatible with it. Simultaneous densification and integration is discussed through mathematical adjustment models in which the geometrical strength of networks is underscored. The rationale behind densifying and integrating networks either in two different steps or simultaneously is analyzed. It is concluded that the simultaneous approach should be avoided unless the various solutions turn out to be statistically compatible.
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References
G. BLAHA (1974): “Influence de l’incertitude des paramètres tenus fixes dans une compensation sur la propagation des variances-covariances”. Bulletin Géodésique, 113, pp. 307–315.
G. BLAHA (1976): “The least-squares Collocation from the Adjustment Point of View”. Scientific report No. 1, DBA Systems Inc.
G. BOMFORD (1985): “Geodesy 4-th edition”. Clarendon press, Oxford.
M. CRAYMER, and P. VANIČEK (1987): “NETAN: A Program for the Interactive Analysis of Geodetic Networks”. IAG Symposium, IUGG General Assembly, Vancouver.
P. DARE, and P. VANIČEK (1982): “Strength Analysis of Horizontal Networks Using Strain”. Meeting of Study Group 5A of FIG, Aalborg University.
E. GRAFAREND, A. KLEUSBERG, and F. MASSMANN (1983): “An Improvement of the Free Satellite Doppler Network Adjustment”, IAG Symposium Proceedings, OSU.
A. LEICK (1984): “Macrometer Satellite Surveying”. Journal of Surveying Engineering, Vol. 110, No. 2.
F.N. LUGOE (1984): “Strain Effects of the Existing Network on the Densification Network”. Paper No. G31-01, AGU Spring Meeting. In EOS Transactions, Vol. 65, No. 16.
F.N. LUGOE (1985): “Rigorous Densification of Horizontal Geodetic Networks”. Technical Report No. 118, Department of Surveying Engineering, UNB, Predericton.
F.N. LUGOE (1987): “Some Experiences With the Strain Analysis of Rigorously Adjusted Densification Networks”. Manuscripta Geodaetica Vol. 12, No. 2.
E. MIKHAIL (1976): “Observations and Least Squares”. Harper and Row, New York
H.B. PAPO (1973): “Considered Parameters in a Least-Squares Adjustment Process”. Bulletin Géodésique, 107, pp. 89–95.
R.R. STEEVES (1984): “Mathematical Models for Use in the Readjustment of the North American Geodetic Networks”. Technical Report No. 1, Geodetic Surveys of Canada, Ottawa.
D.B. THOMSON (1976): “Combination of Geodetic Networks”. Technical Report No. 30, Department of Surveying Engineering, UNB, Fredericton.
J.M. TIENSTRA (1956): “Theory of the Adjustment of Normally Distributed Observations”. Angus, Amsterdam.
P. VANIČEK, and E.J. KRAKIWSKY (1982): “Geodesy: the Concepts”. North Holland, Amsterdam.
P. VANIČEK and F.N. LUGOE (1986): “Rigorous Densification of Horizontal Networks”. Journal of Surveying Engineering, Vol. 112, No. 1.
D.E. WELLS, E.J. KRAKIWSKY, and D.B. THOMSON (1974): “Internal and External Consistency of Doppler, Satellite-Triangulation and Terrestrial Networks”. The Canadian Surveyor Vol. 28, No. 5.
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Lugoe, F.N. Rigorous mathematical models for the densification and integration of geodetic networks. Bull. Geodesique 64, 219–229 (1990). https://doi.org/10.1007/BF02519177
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DOI: https://doi.org/10.1007/BF02519177