Second-Order Response
Sensors that exhibit a second-order deviation from a linear transfer function produce outputs that are proportional to the square of the input intensity. The presence of quadratic non-linearity in an accelerometer causes a rectifying error when the device is subjected to dynamic vibrations. This error manifests as a shift in the apparent zero-g bias under vibration.
The magnitude of this effect is defined by the second-order coefficient in the sensor calibration model.
Vibration Rectification
In dynamic environments, high-frequency oscillations can be rectified into a slow-moving bias shift that degrades navigation accuracy. For an accelerometer with quadratic non-linearity, this shift occurs because the positive peaks of the vibration are amplified differently than the negative peaks. This asymmetry creates a net direct-current offset in the output signal.
This rectification error is difficult to filter out since it lies in the same frequency band as the true motion.
Modeling Correction
Multi-point calibration procedures are executed to identify the quadratic coefficient so that it can be compensated in the sensor output equation. To measure quadratic non-linearity, the sensor is subjected to accelerations of varying magnitudes both positive and negative using a centrifuge or a high-amplitude shaker. The resulting data points are fitted to a second-order polynomial using regression techniques.
Once computed, the correction coefficient is saved in the register of the sensor to linearize the real-time measurements. This correction is verified by measuring the sensor output across its full dynamic range.
Testing Validation
Final testing verifies that the linearized sensor meets the linearity specifications before shipment. For a sensor with compensated quadratic non-linearity, the residual non-linearity must fall below a specified percentage of the full-scale output. This test ensures that the sensor maintains its high accuracy even when operating in high-vibration applications.
