Unscented Transformation based estimation of parameters of nonlinear models using heteroscedastic data

Taubin, 1991, Estimation of planar curves, surfaces, and nonplanar space curves defined by implicit equations with applications to edge and range image segmentation, IEEE Trans. Pattern Anal. Mach. Intell., 13, 1115, 10.1109/34.103273 Zhang, 2000, A flexible new technique for camera calibration, IEEE Trans. Pattern Anal. Mach. Intell., 22, 1330, 10.1109/34.888718 Manoranjan Majji, John Junkins, Total least squares estimation of dynamical systems, in: AIAA Guidance, Navigation, and Control Conference and Exhibit, 2007. Bates, 2007 Laird, 1964, Dynamics of tumor growth, Br. J. Cancer, 18, 490, 10.1038/bjc.1964.55 Kanatani, 2011, Hyper least squares fitting of circles and ellipses, Comput. Stat. Data Anal., 55, 2197, 10.1016/j.csda.2010.12.012 B. Matei, Heteroscedastic errors-in-variables models in computer vision (Ph.D thesis), Department of Electrical and Computer Engineering, Rutgers University, New Brunswick, N.J., May 2001, 〈http://www.caip.rutgers.edu/riul/research/theses.html〉. Chojnacki, 2004, From fns to heiv, IEEE Trans. Pattern Anal. Mach. Intell., 26, 264, 10.1109/TPAMI.2004.1262197 Matei, 2006, Estimation of nonlinear errors-in-variables models for computer vision applications, IEEE Trans. Pattern Anal. Mach. Intell., 28 Kanatani, 1996 Kanatani, 2008, Statistical optimization for geometric fitting, Int. J. Comput. Vis., 80, 167, 10.1007/s11263-007-0098-0 Prasad, 2013, Ellifit, Pattern Recognit., 46, 1449, 10.1016/j.patcog.2012.11.007 Al-Sharadqah, 2012, A doubly optimal ellipse fit, Comput. Stat. Data Anal., 56, 2771, 10.1016/j.csda.2012.02.028 Kanatani, 2008, Statistical optimization for geometric fitting, Int. J. Comput. Vis., 80, 167, 10.1007/s11263-007-0098-0 M.J. Harker, P.L. O׳Leary, First order geometric distance (the myth of Sampsonus), in: Proceedings of the British Machine Vision Conference, BMVA Press, Edinburgh, 2006. pp. 10.1–10.10, http://dx.doi.org/10.5244/C.20.10. Sampson, 1982, Fitting conic sections to very scattered data, Comput. Graph. Image Process., 9, 97, 10.1016/0146-664X(82)90101-0 Julier, 2004, Unscented filtering and nonlinear estimation, Proc. IEEE, 92, 401, 10.1109/JPROC.2003.823141 J.K. Uhlmann, S.J. Julier, A new extension of the Kalman filter to nonlinear systems, in: AeroSense: 11th International Symposium on Aerospace/Defense Sensing, Simulation and Controls, 1997, pp. 182–193. Van Der Klaauw, 2008, Regression–discontinuity analysis, LABOUR, 22, 219, 10.1111/j.1467-9914.2008.00419.x Qiu, 1998, Discontinuous regression surfaces fitting, Ann. Stat., 26, 2218, 10.1214/aos/1024691468 Rosin, 1996, Analysing error of fit functions for ellipses, Pattern Recognit. Lett., 17, 1461, 10.1016/S0167-8655(96)00102-X Rosin, 1998, Ellipse fitting using orthogonal hyperbolae and Stirling׳s oval, Graph. Models Image Process., 60, 209, 10.1006/gmip.1998.0471 Prasad, 2012, Fast segmentation of sub-cellular organelles, Int. J. Image Process. (CSC), 6, 317 Fitzgibbon, 1999, Direct least square fitting of ellipses, IEEE Trans. Pattern Anal. Mach. Intell., 21, 476, 10.1109/34.765658 Kenichi Kanatani, Yasuyuki Sugaya, Compact algorithm for strictly ml ellipse fitting, in: 19th International Conference on Pattern Recognition (ICPR 2008), 8–11 December 2008, Tampa, Florida, USA, IEEE, 2008. pp. 1–4 Zhengyou Zhang, Parameter Estimation Techniques: A Tutorial with Application to Conic Fitting, Rapport de recherche RR-2676, INRIA, October 1995. Ahn, 2001, Least-squares orthogonal distances fitting of circle, sphere, ellipse, hyperbola, and parabola, Pattern Recognit., 34, 2283, 10.1016/S0031-3203(00)00152-7 Kanatani, 2011, Hyper least squares fitting of circles and ellipses, Comput. Stat. Data Anal., 55, 2197, 10.1016/j.csda.2010.12.012 Rosin, 1996, Assessing error of fit functions for ellipses, Graph. Models Image Process., 58, 494, 10.1006/gmip.1996.0041 Chojnacki, 2000, On the fitting of surfaces to data with covariances, IEEE Trans. Pattern Anal. Mach. Intell., 22, 1294, 10.1109/34.888714 Lamé, 2011 Gardiner, 1965, The superellipse, Sci. Am., 213, 222 Berdichevsky, 2011 Bennamoun, 1997, A structural-description-based vision system for automatic object recognition, IEEE Trans. Syst. Man Cybern. Part B: Cybern., 27, 893, 10.1109/3477.650052 Zhang, 2003, Superellipse fitting to partial data, Pattern Recognit., 36, 743, 10.1016/S0031-3203(02)00088-2 Jaffray, 2002, Flat-panel cone-beam computed tomography for image-guided radiation therapy, Int. J. Radiat. Oncol. Biol. Phys., 53, 1337, 10.1016/S0360-3016(02)02884-5 Suetens, 2009 Canny, 1986, A computational approach to edge detection, IEEE Trans. Pattern Anal. Mach. Intell., PAMI-8, 679, 10.1109/TPAMI.1986.4767851 Rosin, 1999, Further five-point fit ellipse fitting, Graph. Models Image Process., 61, 245, 10.1006/gmip.1999.0500