Mathematical Bivariate Polynomial Matrix Fitting for Thermal Drift Compensation
Bivariate polynomial matrix fitting corrects non-linear sensor thermal drift when inputs are normalized and solved via singular value decomposition.
Residual Error Analysis
Calibration Assessment
Mathematical evaluation of regression models examines the discrepancies between measured data and the values predicted by the model. This evaluation, known as residual error analysis, is a standard tool used to verify the accuracy and completeness of sensor calibration curves. It identifies whether any unmodeled systematic patterns remain after the calibration coefficients have been applied.
By highlighting these remaining errors, the technique guides further refinement of the compensation algorithm.
Diagnostic Method
Programmers plot the residuals against the independent variables, such as temperature or applied pressure, to look for non-random patterns. If the residuals are randomly distributed around zero, the calibration model has successfully captured the sensor behavior. Non-random patterns reveal that a higher-order polynomial is required to correct the sensor.
Mathematical Metrics
Statistical measures like the root-mean-square error and the maximum absolute residual quantify the quality of the model fit. These numbers help engineers determine if the calibrated sensor meets the required tolerance limits. They provide an objective metric for comparing different calibration algorithms.
Systematic Boundary
The analysis cannot distinguish between deterministic model errors and random measurement noise if the noise floor is too high. In such cases, the residual plot appears random even though systematic errors may still exist. Testing under highly controlled, low-noise laboratory conditions is required to validate the model.