Estimation of Function Parameters Through Iterated Linearization for Nonlinear Errors-in-variable Regression with Correlated Variables

Accurate measurement uncertainty assessment is a fundamental objective in modern metrology, where fitting data within complex measurement models plays a pivotal role as an initial step in expressing uncertainty. Often, sets of n-tuples of measurements, with the best-estimated values characterizing the measured objects along with their associated uncertainty budget, become available. These data represent direct measurements, construed as realizations of random variables characterized by a joint distribution, which may be fully known or partially known. Here, we present a new modelling approach suitable for a class of measurement problems based on using the errors-in-variables model together with algorithmic implementation in MATLAB.