Bayesian Sensor Calibration of a CMOS-Integrated Hall Sensor Against Thermomechanical Cross-Sensitivities

For the first time, Bayesian sensor calibration is used to identify efficient procedures for a cross-sensitive two parasitic influences. The object under study thermomechanically system determining magnetic induction ${B}$ . packaged comprises Hall sensor, stress and temperature sensor. three signals are combined in polynomial response model with 11 parameters determine compensated offset cross-sensitivities. calibration, sensors exposed mechanical values between 0 −68 MPa, temperatures −40 notation="LaTeX">$100 ^{\circ} \text{C}$ , −25 25 mT. A sample of 35 serves extract prior parameter distribution their fabrication run. experimental design applied sets 2–8 optimal conditions I-optimality G-optimality. inference then allows obtain posterior any uncalibrated from same Any such thereby turned into measuring device individually quantified accuracy. method was successfully 15 validation sensors. In case I-optimality, median root-mean-square (rms) textsigma ±1 σ confidence intervals extracted were found be 113–71 notation="LaTeX">$\mu \text{T}$ after near-I-optimal calibrations based on measurements. Over entire range notation="LaTeX">$| {B} | \leq $ mT, corresponding experimentally determined medians rms deviations predicted 89–71 Analogous observations apply short, made it possible functional known accuracy significantly fewer measurements than parameters. This enabled by knowledge collected thorough characterization prior-generating specimens.