A better least-squares method when both variables have uncertainties

Abstract

The generalized least-squares problem, in which an observation vector satisfies a set of equations that may be nonlinear and implicit, and all components may be subject to errors, can be solved as a constrained minimization problem. When the analysis is specialized to the important case of one-dimensional curve fitting to measurements where both variables contain errors, it becomes similar to the effective variance method. A standard least-squares computer program can be used to apply the new method; the results are superior to these of the effective variance technique. A simple geometrical construction illustrates the principles of the new method.