  The estimate of coefficients of the Convection-Diffusion Equation (CDE) from
experimental measurements belongs in the category of inverse problems, which
are known to come with issues of ill-conditioning or singularity. Here we
concentrate on a particular class that can be reduced to a linear algebraic
problem, with explicit solution. Ill-conditioning of the problem corresponds to
the vanishing of one eigenvalue of the matrix to be inverted. The comparison
with algorithms based upon matching experimental data against numerical
integration of the CDE sheds light on the accuracy of the parameter estimation
procedures, and suggests a path for a more precise assessment of the profiles
and of the related uncertainty. Several instances of the implementation of the
algorithm to real data are presented.

Plasma Physics