  We propose a model-independent framework for fitting hadronic form-factor
data, which is often only available at discrete kinematical points, using
parameterisations based on to unitarity and analyticity. In this novel approach
the latter two properties of quantum-field theory regulate the ill-posed
fitting problem and allow model-independent predictions over the entire
physical range. Kinematical constraints, for example for the vector and scalar
form factors in semileptonic meson decays, can be imposed exactly. The core
formulae are straight-forward to implement with standard math libraries. We
take account of a generalisation of the original Boyd Grinstein Lebed (BGL)
unitarity constraint for form factors and demonstrate our method for the
exclusive semileptonic decay $B_s\to K \ell \nu$, for which we make a number of
phenomenologically relevant predictions, including the CKM matrix element
$|V_{ub}|$.
