Calibration Model
Mathematical modeling using two independent variables provides a framework for correcting multi-variable sensor errors. In sensor calibration, bivariate polynomial regression establishes a relationship where a primary sensor reading and an auxiliary temperature measurement serve as inputs to calculate the corrected output. This approach accounts for cross-sensitivity by fitting a continuous surface to calibration data points rather than a single-variable curve.
The process defines the operational boundary within which the instrument meets its stated accuracy.
Parameter Extraction
Determination of coefficients requires gathering data across a grid of known reference states. Least squares estimation solves the system of equations to minimize the sum of squared residuals at each calibration node. The resulting matrix of coefficients is then programmed into the non-volatile memory of the device.
Error Correction
Reducing cross-sensitivity prevents measurement drift in unstable thermal environments. For example, a pressure transmitter exposed to temperature fluctuations utilizes the calculated coefficients to adjust the raw capacitive or piezoresistive reading. The correction formula evaluates the polynomial in real time to isolate the true pressure from thermal effects.
Computational Execution
Execution of the polynomial on low-power microcontrollers demands careful balance between truncation errors and processing overhead. Higher-order terms increase accuracy but run the risk of overfitting and require more arithmetic operations. A second-order or third-order implementation generally achieves the desired balance for industrial transducer applications.
