I have reviewed at least one paper that claims to solve for the 5 parameters of single-diode equation using only (0, Isc), (Vmp, Imp), (Voc, 0), and the zero derivative of P w.r.t. V at Vmp. This is only four constraints in a determination of five-parameters. Even though it's a non-linear system of equations in the parameters, it still suggests that the problem may not be well posed due to non-uniqueness (
https://en.wikipedia.org/wiki/Well-posed_problem). If not done already, then I think it would be a nice addition to the literature to present a very accessible example of non-uniqueness in this inverse problem. Even better would be to outline "how bad" the situation is in practice for the aforementioned approach.
Anyone care to collaborate on such a project? (If done already, then could someone share a reference?)