Bayesian Sensor Calibration

Oliver Paul

MEMS Materials Laboratory, IMTEK, University of Freiburg

Friday, November 18, 2022, 11:00 - 11:59

Building 102 - SR 02-012

The calibration of sensor systems can cause significant costs in terms of time and resources, in particular when cross-sensitivities to parasitic influences are to be compensated. Successful calibration ensures the trustworthy subsequent operation of a sensor system, guaranteeing that its measurands of interest can be inferred from its output signals with specified uncertainty. I will show that this goal can be reached by simplified calibration procedures with fewer calibration conditions than parameters needed to model the device response. This is achieved using Bayesian inference combining the calibration data of a sensor system with statistical prior information about the ensemble to which it belongs. Optimal reduced sets of calibration conditions are identified by the method of Bayesian experimental design.

The method is demonstrated on a Hall-temperature sensor system from Melexis whose nonlinear response model requires seven parameters in the temperature range between –30 °C and 150 °C and for magnetic field values between –25 mT and 25 mT. For the prior, a multivariate normal distribution of the model parameters is acquired using a sample of specimens drawn from the sensor ensemble. Calibration at only one, two, and three G-optimal calibration conditions improves the accuracy of the magnetic field inferred from sensor output signals by factors of 4, 7, and 10, respectively, over the entire operating range.

I will discuss how to implement the Bayesian prior acquisition, inference, and experimental design, and address technical questions associated with these steps as well as the role of errors in (the independent) variables.