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.
Coefficient Scaling
Arithmetic Adjustment
Mathematical optimization techniques adjust numerical parameters to fit within the constraints of fixed-point arithmetic systems. In sensor signal processors, coefficient scaling transforms floating-point parameters into integer representations that maintain maximum mathematical resolution. This operation utilizes bit-shifting and normalization to preserve the precision of critical sensor calibration curves.
It maps the dynamic range of the coefficients to the word length of the arithmetic logic unit.
Precision Allocation
Embedded processors frequently execute arithmetic on integers rather than slow floating-point units. To execute scaling, each floating-point parameter is multiplied by a power of two before conversion to a binary integer. This shifts the binary point to the right, effectively scaling the value to fill the available register width.
Overflow Protection
Calculation of sensor responses involves the multiplication of scaled coefficients by high-resolution measurement inputs. If the scaling factor is set too high, the intermediate results can exceed the capacity of the accumulation register. Programmers verify the arithmetic limits during firmware design to prevent such arithmetic overflows from corrupting the sensor output.
Resolution Tradeoff
Increasing the scaling factor improves calculation accuracy but reduces the maximum input magnitude that the system can process. If the scaling factor is too low, quantization noise dominates and degrades the overall signal-to-noise ratio. The optimal scaling value balances these conflicting demands.