MATLAB implementation for evaluation of measurements by the generalized method of least squares

The method of Least Squares is one of the fundamental tools in scientific investigation. In 2002, Lars Nielsen described a technique for applying it in its more generalized form, fully compatible with the principles for evaluation of measurement uncertainty. Despite the importance of this contribution, its application has hardly been widespread, probably due to the technicalities of its implementation. Those difficulties are found in an iteration process that contains a near-singular system of equations. In this paper, the work of Nielsen has been reformulated in accordance with the notation of the ISO 'Guide to the expression of uncertainty in measurement', analyzed in detail to solve the implementation difficulties, completed with an adequate convergence criterion, and implemented in the MATLAB mathematical program. The result is a practical tool that will allow the application of the general least-squares method in accordance with the international requirements of expressing the measurements with their uncertainties.