Fitting Two Concentric Circles and Spheres to Data by l1 Orthogonal Distance Regression

The problem of fitting two concentric circles and spheres to data arise in computational metrology. The most commonly used criterion for this is the Least Square norm. There is also interest in other criteria, and here we focus on the use of the l1 norm, which is traditionally regarded as important when the data contain wild points. A common approach to this problem involves an iteration process which forces orthogonality to hold at every iteration and steps of Gauss-Newton type. However, a simple and robust algorithm assigned for using the l1 Orthogonal Distance Regression will be proposed in this paper. The efficient algorithm is demonstrated by some numerical example. Mathematics Subject Classification: 65D10