This might sound like an experimental physics question but I am more interested in a mathematical algorithm solution to the problem.
I have measured spectra of reference compounds which I would like to fit to the spectra of unknown compounds to determine the proportion of each reference in the unknown. The spectra cannot be described by a simple analytical function but rather are fingerprints of endmembers. The unknown compound is likely a mixture of one or more reference compounds. I am interested in the mathematical formalism of an algorithm which might achieve this. Psuedo mathematically the problem might be described as:
$$Experimental(x) = A(Reference_{1}(x)) + B(Reference_{2}(x)) + C$$
where $Experimental(x)$ is a vector containing the experimental data. $Reference_1(x)$ & $Reference_2(x)$ are the reference vectors suitably normalised. $A$ & $B$ are the coefficients to be determined which will be constrained such that $A$ & $B$ are positive and finite. $C$ is a d.c offset.
Can someone point me in the direction of the correct mathematical terminology which might help me find a this? All discussions on least-squares fitting I've come across only deal with the fitting of analytical functions to data not data to data.
Thanks