A class of methods for fitting a curve or surface to data by minimizing the sum of squares of orthogonal distances

Given a family of curves or surfaces in Rs, an important problem is that of finding a member of the family which gives a “best” fit to m given data points. A criterion which is relevant to many application areas is orthogonal distance regression, where the sum of squares of the orthogonal distances from the data points to the surface is minimized. For certain types of fitting problem, attention has recently focussed on the use of an iteration process which forces orthogonality to hold at every iteration and uses steps of Gauss–Newton type. Within this framework a number of different methods has recently emerged, and the purpose of this paper is to place these methods into a unified framework and to make some comparisons.