Mapping Complexity
Sensor behaviors where a single temperature value corresponds to multiple possible output states prevent a simple one-to-one correction. This non-bijective thermal response typically arises when a sensor exhibits memory effects or path dependency. It makes standard polynomial compensation insufficient for high-precision applications.
Hysteresis Identification
The sensor output for a given temperature might differ depending on whether the device is warming up or cooling down. A non-bijective thermal response creates a loop in the calibration curve. This phenomenon is often caused by mechanical stress or material phase changes.
Modeling Approach
Correcting for a non-bijective thermal response requires a model that includes the history of the temperature changes. Simple lookup tables fail because they cannot distinguish between the two paths. Instead, the algorithm must track the previous state and the direction of the thermal trend.
This adds complexity to the firmware but is necessary for maintaining sub-milligram stability in accelerometers. Advanced filters might use hidden states to represent the internal tension of the sensor package. This ensures the output remains accurate even during rapid thermal cycling.
Material Selection
Choosing materials with low thermal expansion coefficients can minimize the severity of this issue. A non-bijective thermal response is often the limiting factor in the performance of industrial grade sensors.
