On the Gauss-Newton method for L1 orthogonal distance regression

The problem of fitting a curve or surface to data has many applications. There are also many fitting criteria which can be used, and one which is widely used in metrology, for example, is that of minimizing the least squares norm of the orthogonal distances from the data points to the curve or surface. The Gauss–Newton method, in correct separated form, is a popular method for solving this problem. There is also interest in alternatives to least squares, and here we focus on the use of the l1 norm, which is traditionally regarded as important when the data contain wild points. The effectiveness of the Gauss–Newton method in this case is studied, with particular attention given to the influence of zero distances. Different aspects of the computation are illustrated by consideration of two particular fitting problems.