I am hoping someone can refer me to a text reference, forum, or other online resource describing the following question. I thought this forum might be a good place to start, but apologies if I was mistaken.
I am designing a sensor with the goal of mapping output sensor values (i.e. data that the sensors spit out to the MCU) into input sensor signals (i.e. the real-world values the sensor is sensing). However, the design of the sensor itself is highly non-linear. In other words, I have no mathematical model to describe how the input goes to --> the output, or vice-versa.
Let me simplify my description. If I were building a gram scale, I would use a strain gauge on a beam combined with the physical/mathematical knowledge that more weight on the scale means a higher value from the strain gauge sensor. Eventually, I could tune and scale my sensor and sensing computer architecture to get me a system that gives me my input from my output.
Now, however, I have a black-box sensor. In other words, the 'weight' values map to the 'sensor' values in non-intuitive ways; more 'weight' on the scale might decrease the sensor value! On top of that, I want to measure an arbitrary number of weights with an arbitrary number of sensors. I am afraid I am being to vague, so I will describe one possible implementation of this design.
Imagine you had a system with J number of Xcm x Ycm sensing pads arranged in whatever configuration you like (hexagon, non-symmetrical, whatever). The only sensors you are allowed to use are K number of FSRs mounted on a common base of all J sensing pads, but you desire to know the weight on each pad.
Now imagine I run 1000 trials on this system, all at different weights on each of the pads. I have the input and output data for each trial, but I do not know how they map to each other. What I am asking is, is there a way to map the input and output to each other so that, given a certain output I have not explicitly tested before, I can predict the input?
Is there a field of research describing this problem? Statistics? Machine learning? Simple polynomial fitting?
Any knowledge out there? Many thanks.