We present preliminary results on an inversion scheme that can be applied to polarimetric measurements of forbidden lines formed in the solar corona. We aim to find optimal fits to synthetic CLE data, delivering information on the vector magnetic field, thermal properties and line of sight position from a single point in the corona. The azimuthal angle is derived from the linear polarization and the line-of-sight magnetic fields are derived via the magnetograph formulation. Our method complements these calculations to achieve full vector magnetic fields. We create a database of emergent Stokes profiles from a Monte Carlo exploration of the parameter space. In building the database set, we first reduce the line formation problem to an irreducible form, factoring out linear parameters such as the magnetic field strength, and using native symmetries in the line formation problem to reduce the dimensionality of the needed calculations. We “precondition” the observed data with simple linear transformations and a rotation of the Stokes profiles around the line-of-sight axis through Sun center, which affects only the linearly polarized components. We show that calculations confined to the ecliptic plane are sufficient to explore the full 3D space. After the best-fit profiles are found, the necessary transformations are applied in reverse to the matching geometric, magnetic and thermal parameters to estimate them in 3D space. We then highlight the natural degeneracies in the analysis and examine their accuracy and sensitivity to noise.