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.
Matrix Inversion Error
Numerical Instability
Mathematical divergence occurring during the resolution of a system of linear equations arises when a matrix is close to being singular. An excessive matrix inversion error occurs when small rounding inaccuracies or measurement noise are amplified during the calculation of the inverse matrix. This issue frequently affects multi-sensor calibration systems where cross-sensitivity coefficients are resolved through simultaneous linear equations.
Computation Vulnerability
When the sensor channels are highly correlated, the coefficient matrix becomes ill-conditioned, which means that the condition number is extremely high. In such cases, the calculation yields unstable results that do not accurately represent the true physical parameters of the sensing array.
Precision Limit
Using single-precision floating-point arithmetic instead of double-precision worsens the issue by introducing larger truncation errors during each step of the calculation.
Correction Technique
Regularization methods, such as Tikhonov regularization, are applied to the matrix before inversion to stabilize the calculation by adding a small diagonal perturbation. This approach trades a small, controlled amount of bias for a large reduction in variance, producing more stable and reliable calibration coefficients. The resulting algorithm is verified by comparing the calculated sensor outputs against reference standards to ensure that the error lies within acceptable metrological bounds.