A systematic MEMS sensor calibration framework

In this paper we present a systematic method to determine sets of close to optimal sensor calibration points for a polynomial approximation. For each set of calibration points a polynomial is used to fit the nonlinear sensor response to the calibration reference. The polynomial parameters are calculated using ordinary least square fit. To determine the quality of each calibration, reference sensor data is measured at discrete test conditions. As an error indicator for the quality of a calibration the root mean square deviation between the calibration polynomial and the reference measurement is calculated. The calibration polynomials and the error indicators are calculated for all possible calibration point sets. To find close to optimal calibration point sets, the worst 99 % of the calibration options are dismissed. This results in a multi-dimensional probability distribution of the probably best calibration point sets. In an experiment, barometric MEMS (micro-electromechanical systems) pressure sensors are calibrated using the proposed calibration method at several temperatures and pressures. The framework is applied to a batch of six of each of the following sensor types: Bosch BMP085, Bosch BMP180, and EPCOS T5400. Results indicate which set of calibration points should be chosen to achieve good calibration results.