Standard Uncertainty estimation on polynomial regression models

Polynomial regression model is very important in the modeling and characterization of sensors. The uncertainty propagation through the polynomial nonlinearity can only be estimated through numerical simulation or linearization approximation according to the Guide to the expression of Uncertainty in Measurement. This paper developed a general cookbook style guide to derive the analytical expression of uncertainty propagating through the polynomial regression models. The proposed method can be easily incorporated into any computer algebra system for reliable and fast evaluation. Specific expressions are derived explicitly for some of the most commonly used low order polynomial regression models. The framework is applied to a few recently published sensor and measurement system models.