A New Regularized Solution to Ill-Posed Problem in Coordinate Transformation

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References

[1] E. W. Grafarend, F. Krumm and F. Okeke, “Curvilinear Geodetic Datum Transformations,” Z Vermessungswesen, Vol. 120, No. 4, 1995, pp. 334-350.

[2] P. Vanicek and R. R. Steeves, “Transformation of Coordinates between Two Horizontal Geodetic Datum,” Journal of Geodesy, Vol. 70, No. 11, 1996, pp. 740-745.

[3] P. Vanicek, P. Novak and R. Craymerm, “On the Correct Determination of Transformation Parameters of Horizontal Geodetic Datum,” Geomatica, Vol. 56, No. 4, 2002, pp. 329-340.

[4] Y. Yang, “Robust Estimation of Geodetic Datum Transformation,” Journal of Geodesy, Vol. 73, No. 9, 1999, pp. 268-274. doi:10.1007/s001900050243

[5] E. W. Grafarend and L. J. Awange, “Nonlinear Analysis of the Transformational Datum Transformation,” Journal of Geodesy, Vol. 77, 2003, pp. 66-76.
doi:10.1007/s00190-002-0299-9

[6] A. N. Tikhonov, “Regularization of Ill-Posed Problems,” Doklady Akademi Nauk, Vol. 151, No. 1, 1963, pp. 49- 52.

[7] A. N. Tikhonov, “Solution of Incurrectly Formulated Pro- blems and the Regularization Method,” Doklady Akade- mi Nauk, Vol. 151, No. 3, 1963, pp. 501-504.

[8] G. H. Golub and C. Reinsch, “Singular Value Decomposition and Least Squares Solutions,” Numerical Mathematics, Vol. 14, 1970, pp. 403-420.
doi:10.1007/BF02163027

[9] P. C. Hansen, “The Truncated SVD as a Method for Re- gularization,” BIT, Vol. 27, 1987, pp. 534-553.
doi:10.1007/BF01937276

[10] P. L. Xu and R. Rummel, “Generalized Ridge Regression with Applications in Determination of Potential Fields,” Manuscripta Geodaetica, Vol. 20, No. 1, 1994, pp. 8-20.

[11] P. L. Xu, Y. Fukuda and Y. Liu, “Multiple Parameter Regularization: Numerical Solution and Application to the Determination of Geopotential from Precise Satellite Orbits,” Journal of Geodesy, Vol. 80, No. 1, 2006, pp. 17-27. doi:10.1007/s00190-006-0025-0

[12] G. H. Golub and C. F. Van Loan, “Matrix Computation,” 3rd Edition, The Johns Hopkins University Press, Baltimore, 1996.

[13] P. C. Hansen, “Rank-Deficient and Discrete Ill-Posed Pro- blems,” SIAM, Philadelphia, 1998.
doi:10.1137/1.9780898719697

[14] P. Tarantola, “Inverse Problem Theory,” SIAM, Philadelphia, 2005.

[15] P. C. Hansen, “The Discrete Picard Condition for Discrete Ill-Posed Problems,” BIT, Vol. 30, No. 4, 1990, pp. 658-672. doi:10.1007/BF01933214

[16] P. C. Hansen, “Truncated SVD Solutions to Discrete Ill- Posed Problems with Ill-Determined Numerical Rank,” Journal on Scientific and Statistical Computing, Vol. 11, 1990, pp. 503-518. doi:10.1137/0911028

[17] P. C. Hansen, “Analysis of Discrete Ill-Posed Problems by Means of the L-Curve,” SIAM Review, Vol. 34, No. 4, 1992, pp. 561-580. doi:10.1137/1034115

[18] M. Hanke, “Limitations of the L-Curve Method in Ill- Posed Problems,” BIT, Vol. 36, No. 2, 1996, pp. 287-301.
doi:10.1007/BF01731984

[19] P. L. Xu, “Truncated SVD Methods for Discrete Linear Ill-Posed Problems,” Geophysical Journal International, Vol. 135, No. 2, 1998, pp. 505-514.
doi:10.1046/j.1365-246X.1998.00652.x

[20] Y. Z. Shen and B. F. Li, “Regularized Solution to Fast GPS Ambiguity Resolution,” Journal of Surveying Engineering, Vol. 133, No. 4, 2007, pp. 168-172.
doi:10.1061/(ASCE)0733-9453(2007)133:4(168)

[21] T. Regińska, “Regularization of Discrete Ill-Posed Problems,” BIT, Vol. 44, No. 3, 2004, pp. 119-133.

[22] G. H. Golub, M. T. Heath and G. Wahba, “Generalized Cross-Validation as a Method for Choosing a Good Ridge Parameter,” Technometrics, Vol. 21, No. 2, 1979, pp. 215- 223. doi:10.2307/1268518