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Sensitivities and Variances for Fitted Parameters of Spheres



Christoph J. Witzgall, Marek Franaszek


Experimental data have been gathered by applying 3D imaging systems, such as LIDAR/LADAR instruments, to spherical objects. This report provides a compilation of the statistical and analytical procedures to be used for an evaluation, to be reported separately, of two different methods of modeling objects, directional and orthogonal fitting, based on those data. Estimating the variances of fitted parameters directly from their sensitivities to data perturbations is proposed. Sensitivities are determined by implicit differentiation of error gradiens. Detailed descriptions of the directional and orthogonal fitting methods, as applied to spheres in a scanning environment, are set forth. In particular, the report furnishes closed-form expressions for those derivatives of the respective error functions which are needed for the calculation of the parameter sensitivities with respect the full set of control variables.
NIST Interagency/Internal Report (NISTIR) - 7616
Report Number


3D imaging systems, directional fitting, least squares, LIDAR/LADAR, orthogonal distance fitting, parameter variance, parameter sensitivity, sphere, statistical modeling


Witzgall, C. and Franaszek, M. (2009), Sensitivities and Variances for Fitted Parameters of Spheres, NIST Interagency/Internal Report (NISTIR), National Institute of Standards and Technology, Gaithersburg, MD, [online], (Accessed April 14, 2024)
Created July 1, 2009, Updated February 19, 2017