Sensitivity Analysis for Gaussian-Associated Features

This paper is concerned with the evaluation of the uncertainties associated with Gaussian-associated features following the GUM methodology. We show how sensitivity matrices necessary for a GUM uncertainty evaluation can be calculated and how the variance matrices associated with the feature parameters can be estimated for a range of complete and partial features common in engineering. Example results are given in tables that allow practitioners to estimate, a priori, the uncertainties associated with fitted parameters, given a proposed measurement strategy for the case in which the point-cloud variance matrix is a multiple of the identity matrix. The sensitivity matrices can be used to evaluate the uncertainties for associated features for more general point-cloud variance matrices. All the calculations involved are direct and involve no optimization or Monte Carlo sampling; they can be implemented in spreadsheet software, for example.