On weighted total least-squares adjustment for linear regression

Journal of Geodesy

Volumn 82, Issue 7, 2008, Pages 415-421

  Schaffrin, Burkhard ^a   Wieser, Andreas ^b  

^a OHIO STATE UNIVERSITY   (United States)

^b GRAZ UNIVERSITY OF TECHNOLOGY   (Austria)

Author keywords

Errors in variables model; Heteroscedastic observations; Multiple linear regression; Straight line fit; Total least squares solution (TLSS); Weight matrix

Indexed keywords

ALGORITHM; COVARIANCE ANALYSIS; GEODESY; LEAST SQUARES METHOD; MULTIPLE REGRESSION;

EID: 43149110257     PISSN: 09497714     EISSN: 14321394     Source Type: Journal    
DOI: 10.1007/s00190-007-0190-9     Document Type: Article

References (16)

1. Golub GH, van Loan Ch (1980) An analysis of the total least-squares problem. SIAM J Num Anal 17: 883-893
2. Golub GH, van Loan Ch (1996) Matrix computations, 3rd edn. Johns Hopkins University Press, Baltimore
3. Grafarend E, Schaffrin B (1993) Adjustment computations in linear models (in German). Bibliographical Institute, Mannheim, Germany
4. Magnus JR, Neudecker H (1988) Matrix differential calculus with applications in statistics and econometrics. Wiley, New York
5. Mann ME, Emanuel KA (2006) Atlantic hurricane trends linked to climate change. EOS 87-24: 233-241
6. Markovsky I, Rastello M, Premoli A, Kukush A, van Huffel S (2006) The element-wise weighted total least-squares problem. Comput Statist Data Anal 50: 181-209
7. Neri F, Saitta G, Chiofalo S (1989) An accurate and straightforward approach to line regression analysis of error-affected experimental data. J Phys Ser E: Sci Instr 22: 215-217
8. Pope AJ (1972) Some pitfalls to be avoided in the iterative adjustment of nonlinear problems. In: Proc 38th Ann Meet Am Soc Phot, Washington, DC, pp 449-473
9. Schaffrin B, Wang Z (1995) Multiplicative outlier search using homBLUP and an equivalence theorem. Manus Geodaet 20: 21-26
10. Schaffrin B, Lee IP, Felus Y, Choi YS (2006) Total least-squares for geodetic straight-line and plane adjustment. Boll Geod Sci Aff 65: 141-168
11. Schaffrin B, Felus Y (2007) Multivariate total-least squares adjustment for empirical affine transformations. In: Proc 6th Hotine-Marussi Symp, Wuhan, People's Republic of China, May, forthcoming
12. Schuermans M, Markovsky I, van Huffel S (2007) An adapted version of the element-wise weighted total least-squares method for applications in cheomometrics. Chemometrics Intell Lab Syst 85: 40-46
13. van Huffel S, Vandewalle J (1991) The total least-squares problem. Computational aspects and analysis. SIAM, Philadelphia
14. van Huffel S, Vandewalle J (1989) Analysis and properties of the generalized total least-squares problem AX ≈ B when some or all columns of A are subject to error. SIAM J Matrix Anal Appl 10: 294-315
15. Xu P (1999) Despeckling SAR-type multiplicative noise. Int J Remote Sensing 20: 2577-2596
16. Xu P, Shimada S (2000) Least-squares parameter estimation in multiplicative noise models. Commun Statist B 29: 83-96