An algorithmic approach to the total least-squares problem with linear and quadratic constraints

Studia Geophysica et Geodaetica

Volumn 53, Issue 1, 2009, Pages 1-16

  Schaffrin, Burkhard ^a   Felus, Yaron A ^b  

^a OHIO STATE UNIVERSITY   (United States)

^b FERRIS STATE UNIVERSITY   (United States)

Author keywords

Adjustment with constraints; Non convex optimization; Total least squares

Indexed keywords

ALGORITHM; ERROR ANALYSIS; EULERIAN ANALYSIS; GEODETIC DATUM; LEAST SQUARES METHOD; NUMERICAL MODEL; OPTIMIZATION;

EID: 62549146224     PISSN: 00393169     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11200-009-0001-2     Document Type: Article

References (24)

1. Beck A. and Ben-Tal A., 2006. On the solution of the Tikhonov regularization of the total least-squares. SIAM J. Optim., 17, 98-118.
2. Björck A., Heggernes P. and Matstoms P., 2000. Methods for large scale total least-squares problems. SIAM J. Matrix Anal. Appl., 22, 413-429.
3. Dowling E.M., Degroat R.D. and Linebarger D.A., 1992.Total least-squares with linear constraints. Acoustics, Speech, and Signal Processing (ICASSP-92), Vol. 5, 341-344, doi: 10.1109/ICASSP.1992.226613.
4. Eckart C. and Young G., 1936. The approximation of one matrix by another of lower rank. Psychometrika, 1, 211-218.
5. Felus A.Y. and Schaffrin B., 2005. Performing similarity transformations using the Error-In-Variables model. American Society for Photogrammetry and Remote Sensing (ASPRS) Annual Meeting, Baltimore/MD, http://www.asprs.org/conference-archive/baltimore2005/.
6. Golub H.G. and van Loan F.C., 1980. An analysis of the Total Least-Squares problem. SIAM J. Numer. Anal., 17, 883-893.
7. Golub G.H. and van Loan C.F., 1996. Matrix Computations, 2nd Edition. Johns Hopkins University Press, Baltimore/MD.
8. Golub G.H., Hansen P.C. and O'Leary D.P., 1999. Tikhonov regularization and Total Least-Squares. SIAM J. Matrix Anal. Appl., 21, 185-194.
9. Grafarend E. and Schaffrin B., 1974. Unbiased free net adjustment. Surv. Rev., 22(171), 200-218.
10. Guo H., and Renaut R.A., 2002. A regularized total least squares algorithm. In: Van Huffel S. and Lemmerling P. (Eds.), Total Least Squares and Errors-in-Variables Modeling: Analysis, Algorithms and Applications. Kluwer Academic Publishers, Dordrecht, The Netherlands, 57-66.
11. Hansen P.C., 2007. Regularization Tools Version 4.0 for Matlab 7.3, Numer. Algorithms, 46, 189-194 (data and programs available at http://www2.imm.dtu.dk/~pch/Regutools/).
12. Hwang C., Wang C.-G. and Lee L.-H., 2002. Adjustment of relative gravity measurements using weighted and datum-free constraints. Comput. Geosci., 28, 1005-1015.
13. Koch K.-R., 1999. Parameter Estimation and Hypothesis Testing in Linear Models (Second Edition). Springer-Verlag, Berlin.
14. Markovsky I., Rastello M.-L., Premoli A., Kukush A. and van Huffel S., 2006. The element-wise weighted total least-squares problem. Comput. Stat. Data Anal., 50, 181-209.
15. Mikhail E.M., 1976. Observations and Least-Squares. IEP, New York.
16. Schaffrin B., 2006. A note on constrained Total Least-Squares estimation. Linear Alg. Appl., 417, 245-258.
17. Schaffrin B. and Felus Y.A., 2005. On total least-squares adjustment with constraints. In: Sansò F. (Ed.), A Window on the Future of Geodesy. International Association of Geodesy Symposia, 128, Springer-Verlag, Berlin, 175-180.
18. Schaffrin B. and Felus Y.A., 2008. On the multivariate Total Least-Squares approach to empirical coordinate transformations: Three algorithms. J Geodesy, 82, 373-383.
19. Schaffrin B. and Wieser A., 2008. On weighted total least-squares adjustment for linear regression, J. Geodesy, 82, 415-421.
20. Schaffrin B., Lee I., Felus Y.A. and Choi Y., 2006. Total Least-Squares (TLS) for geodetic straight-line and plane adjustment. Bollettino di Geodesia e Scienze Affini, 65(3), 141-168.
21. Sillard P. and Boucher C., 2001. A review of algebraic constraints in terrestrial reference frame datum definition. J. Geodesy, 75, 63-73.
22. Sima D.M., van Huffel S. and Golub G.H., 2004. Regularized total least-squares based on quadratic eigenvalue problem solver. Bit, 44, 793-812.
23. van Huffel S. and Vandewalle J., 1991. The Total Least-Squares Problem, Computational Aspects and Analysis. Society for Industrial and Applied Mathematics, Philadelphia.
24. Yeredor A., 2006. On the role of constraints in system identification. In: Van Huffel S. and Markovsky I. (Eds.), Fourth International Workshop on Total Least-Squares and Errors-in-Variables Modeling, Leuven/Belgium, 46-48 (http://users.ecs.soton.ac.uk/im/workshop/slides.html).