Logo of the Physikalisch-Technische Bundesanstalt
Gateway for politics

Achieving more with less sensor data

Improved estimation of measurement uncertainty for interpolated measurement data

PTB-News 1.2024
Especially interesting for

Temperature measurement

Coordinate metrology

Smart buildings / IoT for buildings

Calibration laboratories

In principle, sensor networks and appropriate interpolation methods can be used to determine the temperature at any desired location in a room. The reliability of such interpolated data was tested at PTB.

Schematic representation of the measuring room with a few sensors. By means of this new method, temperatures and their uncertainties can be estimated at any desired location based on local sensor data.

For this purpose, the geostatistical interpolation method called “kriging” (after Daniel G. Krige) was applied. The known temperatures at the sensor positions are used to determine the best linear unbi-ased estimate of the temperature at a location that is not near a sensor. The interpolated temperature is modeled as a realization of a random variable with an associated mean value and standard deviation. The standard deviation or, in case of changing sensor data, its mean value, can be considered as the interpolation’s contribution to the uncertainty of the estimated temperature.

In order to take into account the uncertainty contributions of the sensors as well, a new method was developed at PTB. If the measurement uncertainties of the individual sensors are known, e.g. from calibrations, their influence on the interpolated values can be determined by means of a Monte Carlo simulation. The values provided by the sensors are randomly changed within the range of their measurement uncertainty and the effect on the interpolated random variable is determined. If this process is repeated frequently enough, the standard deviation of the interpolated temperature caused by the variation in sensor data can be determined.

The new method was demonstrated using an air-conditioned laboratory room with two coordinate measuring machines as an example. The room is equipped with 24 platinum resistance thermometers spread around the space to monitor spatial and temporal temperature variations. As anticipated, the interpolated values and their uncertainties primarily depend on the values of the closest sensor. These values usually have a lower uncertainty. Moreover, this has demonstrated that the method can be used to detect undesired heat sources.

The method is not limited to temperature measurements. It can also be applied to sensor networks for any other measurand. It was deliberately designed to be universal and can, amongst other things, also be used when sensors of different qualities are being combined. Apart from spatial interpolation, temporal interpolation is also possible and can be used to estimate missing measurement values, which ensures a robust reaction in case of potential sensor failures.


Anupam Vedurmudi

Department 9.4

Metrology for Digital Transformation

Phone: +49 531 592-9413
Opens local program for sending emailanupam.vedurmudi(at)ptb.de

Scientific publication

A. P. Vedurmudi, K. Janzen, M. Nagler, S. Eichstaedt: Uncertainty-aware temperature interpolation for measurement rooms using ordinary Kriging. Meas. Sci. Technol. 34, 064007 (2023)