I'm currently using an LUT (Look-Up Table) stored in a microcontroller, to read the temperature from an NTC sensor. I'd like to achieve a precision which is known, it doesn't matter if it is not so high.
The first step in which I'm stuck is to know well the error introduced by evaluating an interpolation of two values in a LUT.
What I thought: If the LUT have 1°C steps, the maximum error using the intermediate value as discriminant, is 0.5°C. And (what I thought) the only final solution to this is that I can print on a display the value interpolated (i.e. 24.8°C) instead of the LUT (i.e. 25°C), but both have 0.5°C of error. The case of 24.8 +- 0.5°C it doesn't seems so meaningful. Maybe 24.5°C could be a better solution.
The second thought is that interpolating using two points separated by 1°C, are bringing an error which can be smaller than 0.5°C, since it is related to the ratio of second derivative of the curve and a factor of 1/8 times the step of the function (here 1°C) (https://en.wikipedia.org/wiki/Linear_interpolation#Linear_interpolation_as_approximation). But I'm not sure at all of what I am reading: supposing that I have the Steinhart-Hart equation, I do not have the second order derivative. Am I right? Any suggestion? Is this analysis necessary to make a correct estiamtion of the error?