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The objective of this work is to propose a new algorithm to fit a sphere on anoisy 3D point cloud distributed around a complete or a truncated sphere. Moreprecisely, we introduce a projected Robbins-Monro algorithm and its averagedversion for estimating the center and the radius of the sphere. We giveasymptotic results such as the almost sure convergence of these algorithms aswell as the asymptotic normality of the averaged algorithm. Furthermore, somenon-asymptotic results will be given, such as the rates of convergence inquadratic mean. Some numerical experiments show the efficiency of the proposedalgorithm on simulated data for small to moderate sample sizes.

An averaged projected Robbins-Monro algorithm for estimating the parameters of a truncated spherical distribution