Polynomial Fitting
Mathematical curves constructed from multiple third-order polynomials provide a smooth and continuous fit for complex calibration data. These piecewise cubic splines connect a series of data points while ensuring that the slope and curvature are consistent at every junction. This method avoids the oscillations that occur when using a single high-degree polynomial for the entire range.
It is the preferred technique for modeling the non-linear response of high precision sensors.
Local Curvature
Each segment of the curve is defined by its own set of coefficients. By using piecewise cubic splines, the system can follow sharp changes in sensor behavior without affecting the fit in other areas. This localized control is necessary for correcting erratic thermal drifts.
Numerical Stability
Splines are less sensitive to small errors in individual calibration points than other fitting methods. Implementing piecewise cubic splines in a sensor microprocessor requires efficient algorithms to solve the polynomial equations quickly. The stability of the fit ensures that the sensor output does not jump between calibration steps.
Calibration Map
The resulting curve forms a map that the sensor uses to convert raw electrical signals into engineering units. Piecewise cubic splines allow for a higher level of accuracy than linear interpolation between points. This map is stored in the sensor memory during the final test phase.
