A rapid algorithm for tomographic inversion is presented that allows post-discharge reconstruction of the soft x-ray (SXR) emissivity evolution in the Tokamak a configuration variable (TCV). Simultaneously, it determines the centre of gravity of the emissivity that may serve as a reliable measurement of the plasma position, that is independent of magnetic measurements. Tests of the algorithm were performed using shaped phantom datasets and all past SXR measurements were processed to obtain plasma position statistics. Multiple linear regression is applied in matching the results with the magnetic axis data. Systematic functionalities including magnetic field dependence and drift of the magnetic axis are observed. The joint resolution limit of magnetic and SXR position measurements at TCV is derived from the residual discrepancies and equals 2.2 and 3.1 mm in the radial and vertical directions, respectively.