Mathematical Approximation
Multi-variable regression modeling calculates a continuous mathematical surface to correct complex sensor errors across simultaneous pressure and temperature spans. By applying a polynomial surface fit, calibration software determines a matrix of coefficients that minimizes the difference between measured sensor outputs and true reference values. This method ensures that the sensor signal conditioner can apply real-time corrections based on localized sensor readings, which dramatically reduces the residual thermal error of the system.
Error Minimization
Measurement data collected during factory calibration always contain small random errors or thermal noise. A polynomial surface fit must not overfit these data points, as this would introduce spurious oscillations between calibrated test temperatures. Selecting the appropriate degree for the polynomial balances sensor accuracy with data-smoothing requirements.
Computational Integration
Embedded microcontrollers in smart sensors have limited memory and processing power to evaluate complex mathematical equations. Running a polynomial surface fit of high order requires efficient firmware that calculates the correction using nested multiplication. This implementation keeps processor cycles low and reduces power consumption.
Extrapolation Risk
Behavior of high-degree algebraic equations becomes highly unpredictable outside the boundaries of the test data. A polynomial surface fit should never be used to predict sensor output beyond the thermal limits verified during calibration. Testing must cover the entire specified range to prevent run-away correction values.
