Half-Blind Calibration for the Efficient Compensation of Parasitic Cross-Sensitivities in Nonlinear Multisensor Systems

We extend the method of half-blind calibration (HBC) to sensor systems with a nonlinear response. HBC ensures the efficient compensation of undesired cross-sensitivities in sensor systems despite a reduced calibration effort. During HBC, one applies load combinations covering the ranges of the measurands of primary interest of the system and the undesired disturbances. However, only the measurand values and the output signals of the individual sensors of the system are recorded. In the proposed nonlinear HBC, these data are fitted using multiple polynomial regression, treating the sensor data as predictor variables and each measurand of interest as the dependent variable. For each such measurand, the extracted polynomial function of the sensor signals predicts cross-sensitivity-compensated values. The method is demonstrated using a silicon-based magnetic sensor system, where stress and temperature constitute disturbances. During calibration, controlled values of the out-of-plane component of the magnetic induction are applied, while stress and temperature are varied without accurate knowledge of their values. Output signals of the Hall sensor and of co-integrated stress and temperature sensors provide the sensor signals. All respond nonlinearly to stress and temperature. Using a polynomial regression of degree 4, the system achieves an accuracy of the measured magnetic induction of $136~\mu \text{T}$ in the ranges of ±21 mT, -40 °C to 125 °C, and up to -80 MPa of in-plane stress. This performance was achieved without quantitative knowledge of the disturbances during calibration. Nonlinear HBC has the potential to considerably simplify calibration equipment and procedures.