Numerical Parameter
Numerical parameters in an algebraic expansion define the specific shape and curvature of a model used for data linearization. Inside the context of sensor calibration, polynomial coefficients weight each power of the input variable to produce a corrected output. These values are derived through a least-squares regression analysis of raw calibration data.
Storing the coefficients in non-volatile memory allows the embedded processor to apply the correction in real time.
Mapping Procedure
Applying the model involves multiplying the sensor signal by the appropriate mathematical weights. When a system utilizes polynomial coefficients, the precision of these numbers must exceed the target accuracy of the measurement to avoid rounding errors. Digital systems often use floating-point arithmetic to maintain the necessary resolution during these calculations.
The resulting value represents the physical quantity in standard engineering units.
Overfitting Prevention
Higher order models can lead to instability if the number of terms is too large relative to the data set. Choosing the correct number of polynomial coefficients requires a balance between reducing the residual error and maintaining a smooth curve. An over-parameterized model might track random noise rather than the underlying physical relationship.
Verification at intermediate points between calibration steps helps confirm the validity of the selected order.
Storage Format
Data storage requirements for the calibration parameters depend on the bit-depth of the processor. Placing polynomial coefficients in a structured memory map allows for easy retrieval by the calculation engine. Each coefficient is typically stored as a thirty-two or sixty-four bit value to preserve the dynamic range of the model.
Updating these values during a re-calibration event requires a secure communication protocol to prevent data corruption.
