Two-Dimensional Linear Comparative Calibration and Measurement Uncertainty

Abstract

We propose a new comparative calibration model with linear calibration function, suggested for comparison of two measurement devices, each measuring two-dimensional signals (measurements), based on using metrological approach to the expression of uncertainty in measurement. The considered errors-in-variables (EIV) model is nonlinear in its parameters. However, after proper linearization, the calibration parameters can be appropriately evaluated by using the optimum statistical estimation techniques suggested for linear regression models with type II restrictions on the model parameters. Based on that, we propose an iterative algorithm for estimating the parameters of the linear calibration function and also a method for evaluation of the uncertainty in measurement with using the calibrated device.