Publication details
Applications of Iterated Linearization for non-linear errors-in-variable regression to metrological data
| Authors | |
|---|---|
| Year of publication | 2025 |
| Type | Article in Periodical |
| Magazine / Source | Measurement: Sensors |
| MU Faculty or unit | |
| Citation | |
| web | https://www.sciencedirect.com/science/article/pii/S2665917424007050 |
| Doi | http://dx.doi.org/10.1016/j.measen.2024.101729 |
| Keywords | Nanoindentation; Curve fitting; Errors-in-variables; Uncertainty analysis |
| Description | Correct data processing and uncertainty assessment is crucial for metrology. One of the most common methods used is function fitting using non-linear least squares. This numerical method has been implemented in probably all data processing software and is quick and easy to use. Unfortunately, it has its limitations – notably it works only for very simple models of the uncertainties present in the system. Uncertainties in the dependent variable cannot be taken into account, and neither do correlations. Errors-in-variables models minimize a generalized distance of the points from the fitted function. The metric used to compute the distance is given by the inverse of the covariance matrix. Thus, the estimates of the uncertainties entering the computation may affect the resulting estimates of the fitted parameters. In this contribution we illustrate the use of an iterative EIV algorithm on an example from nanoindentation, especially the sensitivity of the results to input data including uncertainties. |
| Related projects: |