On the multivariate total least-squares approach to empirical coordinate transformations. Three algorithms

Journal of Geodesy

Volumn 82, Issue 6, 2008, Pages 373-383

  Schaffrin, Burkhard ^a   Felus, Yaron A ^b  

^a OHIO STATE UNIVERSITY   (United States)

^b FERRIS STATE UNIVERSITY   (United States)

Author keywords

Empirical coordinate transformation; Errors in variables modeling; Multivariate total least squares solution (MTLSS); Quasi linear models

Indexed keywords

ALGORITHM; EMPIRICAL ANALYSIS; ERROR ANALYSIS; EULERIAN ANALYSIS; LEAST SQUARES METHOD; MODELING; MULTIVARIATE ANALYSIS; TRANSFORM;

EID: 43149083042     PISSN: 09497714     EISSN: 14321394     Source Type: Journal    
DOI: 10.1007/s00190-007-0186-5     Document Type: Article

References (28)

1. Björck Ǎ. (1997) Newton and Rayleigh quotient methods for total least-squares problems. In: Huffel S(eds) Recent advances in total least-squares techniques and errors-in-variables modeling. SIAM, Philadelphia, pp 149-160
2. Björck Ǎ., Heggernes P, Matstoms P (2000) Methods for large scale total least-squares problems. SIAM J Matrix Anal Appl 22(2):413-429
3. Chen W, Hill C (2005) Evaluation procedure for coordinate transformation. J Surv Eng 131(2):43-49
4. Demmel J, Gu M, Eisenstat S, Slapnićar I, Veselić K, Drmać Z (1999) Computing the singular value decomposition with high relative accuracy. Linear Algebra Appl 299(1-3):21-80
5. Eckart C, Young G (1936) The approximation of one matrix by another of lower rank. Psychometrika 1(3):211-218
6. Felus AY (2007) On the positional enhancement of digital cadastral maps. Surv Rev 39(306):268-281
7. Felus AY, Schaffrin B (2005) A total least-squares approach for semivariogram modeling of aeromagnetic data. In: Cheng Q, Bonham-Carter G(eds) GIS and spatial analysis, IAMG'05. China University of Geosciences Printing House, Beijing, pp 215-221
8. Golub GH, van Loan CF (1980) An analysis of the total least-squares problem. SIAM J Numer Anal 17(6):883-893
9. Helmert FR (1872) Adjustment computation with the least-squares method (in German). Teubner, Leipzig, pp 348
10. Hu WC (2003) Efficient least-squares coordinate transformation for an arbitrary number of parameters. J Surv Eng 129(2):65-72
11. Koch KR (1999) Parameter estimation and hypothesis testing in linear models (2nd edn). Springer, Berlin, pp 333
12. Mikhail EM (1976) Observations and least-squares. IEP, New York, pp 497
13. Mikhail EM, Gracie G (1981) Analysis and adjustment of survey measurements. Van Nostrand Reinhold, New York, pp 340
14. Mikhail EM, Bethel JS, McGlone JC (2001) Introduction to modern photogrammetry. Wiley, New York, pp 479
15. Mirsky L (1960) Symmetric gauge functions and unitarily invariant norms. Q J Math Oxford 11:50-59
16. Pope AJ (1972) Some pitfalls to be avoided in the iterative adjustment of nonlinear problems. In: Proceedings of the 38th Annual Meeting. American Society of Photogrammetry, Washington, pp 449-471
17. Schaffrin B (2006) A note on constrained total least-squares estimation. Linear Algebra Appl 417(1):245-258
18. Schaffrin B, Felus YA (2005) On total least-squares adjustment with constraints. In: Sanso F(eds) A Window on the Future of Geodesy, IAG-Symp, vol 128. Springer, Berlin, pp 417-421
19. Schaffrin B, Felus AY (2007) Multivariate total least-squares adjustment for empirical affine transformations. In: Xu P (ed) Proceedings of the 6th Hotine-Marussi Symposium for theoretical and computational geodesy. Springer, Berlin (forthcoming)
20. Schaffrin B, Lee IP, Felus YA, Choi YC (2006) Total least-squares (TLS) for geodetic straight-line and plane adjustment. Boll Geod Sci Affini 65(3):141-168
21. Schaffrin B, Wieser A (2008) On weighted total least-squares adjustment for linear regression. J Geodesy (in press)
22. Shen YZ, Chen Y, Zheng DH (2006) A quaternion-based geodetic datum transformation algorithm. J Geod 80(5):233-239
23. Sprinsky WH (1987) Transformation of positional geographic data from paper-based map products. Am Cartogr 14(4):359-366
24. Strang G (1988) Linear algebra and its applications, 3rd edn. Harcourt Brace Jovanovich, San Diego, pp 374
25. Teunissen PJG (1989) A note on the bias in the symmetric Helmert transformation. Festschrift to Torben Krarup, Geodetic Institute, Bull. no. 58, Copenhagen, Denmark, pp 335-342
26. Tsenkov T, Gospodinov S (2002) Determination of 2D-tectonic deformations using affine transformation. Zeitsch Vermess 127(4):262-264
27. van Huffel S, Vandewalle J (1991) The total least-squares problem. Computational aspects and analysis. Society for Industrial and Applied Mathematics, Philadelphia, 374 pp
28. Wolf PR, Ghilani CD (1997) Adjustment computations. Statistics and least-squares in surveying and GIS. Wiley, New York, pp 564