Estimation Algorithm
Mathematical optimization methods fit empirical data points to functional models by minimizing the sum of squared discrepancies between observed and calculated values. Calculating least squares regression determines optimal linear or polynomial coefficients for sensor calibration curves based on raw measurement data. Summing squared residual errors ensures that larger deviations carry proportionally greater weight during parameter estimation.
Automated calibration routines use this technique to generate polynomial coefficients for sensor signal conditioners.
Residual Minimization
Matrix inversion techniques resolve linear parameter vectors from overdetermined systems of measurement equations. Singular value decomposition prevents numerical instability during matrix inversion when calibration data contains collinear inputs. Resulting regression coefficients define the best-fit line across measurement points.
Outlier Sensitivity
Extreme outliers disproportionately distort fitted regression curves due to the quadratic weighting of residual errors. Noise spikes or spurious measurement readings force regression parameters away from true sensor responses. Robust fitting methods or data filtering protocols remove spurious outliers before applying least squares computations.
Model Boundary
Fitting validity depends on assumption of normally distributed, homoscedastic measurement noise. Applying least squares regression across non-linear sensor ranges without proper higher-order polynomial terms introduces systematic fitting errors. Residual plots reveal unmodeled sensor non-linearities when residual errors display structured patterns.
