A general solution in geodetic nonlinear rank-defect models;Una soluzione generale per i modelli geodetici non lineari a difetto di rango

Bollettino di Geodesia e Scienze Affini

Volumn 56, Issue 1, 1997, Pages 1-25

  Xu, Peiliang ^a  

^a UNIVERSITY OF CALGARY   (Canada)

Author keywords

Free network; Nonlinearity; Rank defect

Indexed keywords

COORDINATE; GEODESY; GEODETIC NETWORK; NONLINEAR RANK DEFECT ADJUSTMENT;

EID: 0030817233     PISSN: 00066710     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (34)

1. W. BAARDA (1973), S-transformation and criterion matrices. Neth. Geod. Comm. Publ. Geod., New Series, vol. 5, no. 1.
2. G. BLAHA (1971), Inner adjustment constraints with emphasis on range observations. Reports of the Department of Geodetic Sciences, no. 148, Diss., The Ohio State University.
3. G. BLAHA (1982), Free networks: minimum norm solution as obtained by the inner adjustment constraint method. Bulletin Géodésique, vol. 56, pp. 209-219.
4. F. CROSILLA, T. RUSSO, B. SCHAFFRIN (1989), Improved second order design and the datum choice. Bulletin Géodésique, vol. 63, pp. 191-202.
5. X.Z. CUI, D.J. LIU (1986), On applications of free net adjustment in view of datum. J. Wuhan Techn. Uni. Sur. Mapping, 11, no. 2, 1-7 (in Chinese with English abstract).
6. A. DERMANIS (1993), The photogrammetric inner constraints. To appear in ISPRS J. Photog. Rem. Sen.
7. E.W. GRAFAREND, E. KNICKMEYER, B. SCHAFFRIN (1982), Geodätische Datumtransformationen. ZfV, vol. 107, pp. 15-25.
8. E.W. GRAFAREND, B. SCHAFFRIN (1974), Unbiased free net adjustment. Survey Review, 200-218.
9. E.W. GRAFAREND, B. SCHAFFRIN (1976), Equivalence of estimable quantities and invariance in geodetic networks. ZfV, vol. 101, pp. 485-491.
10. E.W. GRAFAREND, B. SCHAFFRIN (1993), Ausgleichung in linearen Modellen. BI Wissenschaftsverlag, Mannheim.
11. P. MEISSL (1962), Die innere Genauigkeit eines Punkthaufens. Öster. ZfV, vol. 50, pp. 159-165, 186-194.
12. P. MEISSL (1965), Über die innere Genauigkeit dreidimensionaler Punkthaufen. ZfV, no. 90, pp. 109-118.
13. P. MEISSL (1969), Zusammenfassung und Ausbau der inneren Fehlertheorie eines Punkthaufens. In: R. Rinner, K. Killian and P. Meissl (eds.), «Beiträge zur Theorie der geodätischen Netze im Raum», DGK, A61, pp. 8-21.
14. P. MEISSL (1982), Least squares adjustment - a modern approach. Mitt. geod. Inst., TU Graz, no. 43.
15. S.K. MITRA, C.R. RAO (1968), Some results in estimation and tests of linear hypotheses under the Gauss-Markoff model. Sankhya-, A30, pp. 281-290.
16. E. MITTERMAYER (1972), A generalization of the least squares method for the adjustment of free networks. Bulletin Géodésique, vol. 46, pp. 139-151.
17. H. PAPO (1987), Bases of null space in analytical photogrammetry. Photogrammetria, vol. 41, pp. 233-244.
18. H. PAPO, A. PERELMUTER (1981), Datum definition by free net adjustment. Bulletin Géodésique, vol. 55, pp. 218-226.
19. H. PELZER (1971), Zur Analyse geodätischer Deformationsmessungen. DGK, C164, München.
20. A. PERELMUTER (1979), Adjustment of free networks. Bulletin Géodésique, vol. 53, pp. 291-296.
21. C.R. RAO, S.K. MITRA (1971), Generalized inverse of matrices and its applications. John Wiley and Sons, New York.
22. K. RINNER (1966), Systematic investigations of geodetic networks in space. European Res. Office, Contract no. 91-591-EUC 3584.
23. B. SCHAFFRIN (1985), Aspects of network design. In: E.W. Grafarend and F. Sansò (eds.), «Optimization and design of geodetic networks», Springer Verlag, Berlin, pp. 548-597.
24. S.R. SEARLE (1971), Linear models. John Wiley and Sons, New York.
25. B.Z. TAO (1991), A unified method of hypothesis test in adjustment models and its application. Acta Geodaetica et Cartographica Sinica, vol. 20, pp. 100-108 (in Chinese with English abstract).
26. P. TEUNISSEN (1985), Zero order design: generalized inverse, adjustment, the datum problem and S-transformations. In: E.W. Grafarend and F. Sansò (eds.), «Optimization and design of geodetic networks», Springer Verlag, Berlin, pp. 11-55.
27. H. WOLF (1963), Geometric connection and re-orientation of three dimensional triangulation nets. Bulletin Géodésique, vol. 37, pp. 165-169.
28. H. WOLF (1972), Helmerts Lösung zum Problem der freien Netze mit singulärer Normalgleichungsmatrix. ZfV, vol. 97, pp. 189-192.
29. H. WOLF (1973), Die Helmert-Inverse bei freien geodätischen Netzen. ZfV, vol. 98, pp. 396-398.
30. P.L. XU (1993), Testability, datum definitions, coordinate systems and free net adjustment. Pres. at 8th Int. Symp. on Recent Crustal Movement, Kobe, Japan, December 6-10.
31. P.L. XU (1994), Testability and adjustment in free net models. J. Geod. Soc. Japan, Supplement issue, pp. 315-320.
32. P.L. XU (1995), Testing the hypotheses of non-estimable functions in free net adjustment models. Manuscripta Geodaetica, vol. 20, pp. 73-81.
33. J.W. ZHOU (1980), Quasi-stable adjustment of monitoring networks. Wuhan Inst. Geod. and Geophys., Spec. Publ., no. 2 (in Chinese).
34. Z.M. ZHOU (1983), Untersuchung der mathematischen Modelle zur Kombination eines terrestrischen Netzes mit einem Satellitennetz. DGK, C274, München.