Orthogonal least squares fitting with cylinders

References

• I.A. Al-Subaihi, An algorithm for fitting circular arcs to data using the l1 norm, Numer. Algorithms 47 (2008), pp. 1–14. doi: 10.1007/s11075-007-9141-z
   Google Scholar
• I.A. Al-Subaihi, An algorithm for matching point sets using the l1 norm, Numer. Algorithms 41 (2005), pp. 203–217. doi: 10.1007/s11075-005-9004-4
   Google Scholar
• I.A. Al-Subaihi and G.A. Watson, Algebraic fitting of quadric surfaces to data, Commun. Appl. Anal. 9 (2005), pp. 539–548.
   Google Scholar
• A. Atieg, Numerical methods for fitting curves and surfaces to data by orthogonal distance regression and some generazations, Ph.D. thesis, University of Dundee, 2005.
   Google Scholar
• A. Atieg and G.A. Watson, A class of methods for fitting a curve or surface to data by minimizing the sum of squares of orthogonal distances, J. Comput. Appl. Math. 158 (2003), pp. 277–296. doi: 10.1016/S0377-0427(03)00448-5
   Web of Science ®Google Scholar
• F. Ding, Combined state and least squares parameter estimation algorithms for dynamic systems, Appl. Math. Model. 38(1) (2014), pp. 403–412. doi: 10.1016/j.apm.2013.06.007
   Web of Science ®Google Scholar
• F. Ding and Y. Gu, Performance analysis of the auxiliary model-based least-squares identification algorithm for one-step state-delay systems, Int. J. Comput. Math. 89(15) (2012), pp. 2019–2028. doi: 10.1080/00207160.2012.698008
   Web of Science ®Google Scholar
• D. Eberly, Fitting 3D Data with a Cylinder, Geometric Tools, Inc., 2003. Available at http://www.geometrictools.com/Documentation/CylinderFitting.pdfhttp://www.geometrictools.com/Documentation/CylinderFitting.pdf.
   Google Scholar
• W. Gander, G.H. Golub, and R. Strebel, Fitting of circles and ellipses: Least squares solution, BIT 34 (1994), pp. 556–577. doi: 10.1007/BF01934268
   Web of Science ®Google Scholar
• J.-F. Guo, Q.-M. Gui, and Y.-X. Yang, Least squares fitting method based on bivariate nonuniform B-spline and its applications in surveying engineering, J. Surv. Eng. 129(3) (2003), pp. 105–109. doi: 10.1061/(ASCE)0733-9453(2003)129:3(105)
   Web of Science ®Google Scholar
• R.J. Hanson and M.J. Norris, Analysis of measurements based on the singular value decomposition, SIAM J. Statist. Comput. 2 (1981), pp. 363–373. doi: 10.1137/0902029
   Web of Science ®Google Scholar
• X. Li, L. Zhou, R. Ding, and J. Sheng, Recursive least-squares estimation for Hammerstein nonlinear systems with nonuniform sampling, Math. Probl. Eng. 2013 (2013), Article ID 240929, 8 pages.
   Google Scholar
• X. Li, L. Zhou, R. Ding, and J. Sheng, Recursive least-squares estimation for Hammerstein nonlinear systems with nonuniform sampling, Int. J. Comput. Math. 90(7) (2013), pp. 1524–1534. doi: 10.1080/00207160.2012.758364
   Web of Science ®Google Scholar
• Y. Liu and R. Ding, Consistency of the extended gradient identification algorithm for multi-input multi-output systems with moving average noises, Int. J. Comput. Math. 90(9) (2013), pp. 1840–1852. doi: 10.1080/00207160.2013.772143
   Web of Science ®Google Scholar
• Y. Liu, F. Ding, and Y. Shi, An efficient hierarchical identification method for general dual-rate sampled-data systems, Automatica 50(3) (2014), pp. 962–970. doi: 10.1016/j.automatica.2013.12.025
   Web of Science ®Google Scholar
• G. Lukács, A. Marshall, and R. Martin, Geometric Least-squares Fitting of Spheres, Cylinders, Cones and Tori, SIAM, 1997. Available at http://ralph.cs.cf.ac.uk/papers/Geometry/fit.pdf.
   Google Scholar
• H. Späth, Least-squares fitting by circles, Computing 57 (1996), pp. 179–185. doi: 10.1007/BF02276879
   Web of Science ®Google Scholar
• H. Späth, Least-squares fitting by ellipses and hyperbolas, Comput. Statist. 12 (1997), pp. 329–341.
   Web of Science ®Google Scholar
• H. Späth, Orthogonal least squares fitting by conic sections, in Recent Advances in Total Least Squares and Errors-in-Variables Techniques, S. Huffel ed., SIAM, Philadelphia, 1997, pp. 259–264.
   Google Scholar
• H. Späth, Least-Square fitting with spheres, J. Optim. Theory Appl. 96(1) (1998), pp. 191–199. doi: 10.1023/A:1022675403441
   Web of Science ®Google Scholar
• H. Späth, Identifying spatial point sets, Math. Commun. 8 (2003), pp. 69–75.
   Google Scholar
• H. Späth, Fitting affine and orthogonal transformations between two sets of points, Math. Commun. 9 (2004), pp. 27–34.
   Google Scholar
• V. Srinivasan, How tall is the pyramid of Cheops …and other problems in computational metrology, SIAM News 29 (1996), pp. 8–9.
   Google Scholar
• R. Strebel, D. Sourlier, and W. Gander, A comparison of orthogonal least squares fitting in coordinate metrology, in Recent Advances in Total Least Squares and Errors-in-Variables Techniques, S. Huffel ed., SIAM, Philadelphia, 1997, pp. 259–264.
   Google Scholar
• D.A. Turner, The approximation of cartesian co-ordinate data by parametric orthogonal distance regression, Ph.D. thesis, University of Huddersfield, 1999.
   Google Scholar
• J.M. Varah, Least squares data fitting with implicit functions, BIT Numer. Math. 36 (1996), pp. 842–854. doi: 10.1007/BF01733795
   Web of Science ®Google Scholar
• H. Yin and H. Zhang, Least squares based iterative algorithm for the coupled Sylvester matrix equations, Math. Probl. Eng. 2014 (2014), Article ID 831321, 8 pages.
   Google Scholar
• D.S. Zwick, Applications of orthogonal distance regression in metrology, in Recent Advances in Total Least Squares and Errors-in-Variables Techniques, S. Huffel ed., SIAM, Philadephia, 1997, pp. 265–272.
   Google Scholar