Examples of the status determination of companion candidates around HD 14943 (left) and η Tuc (HD 224392; right), from astrometric measurements at two different epochs. The positions on the sky are reported in the upper panel: the candidates were first imaged on 2005-11-07 (filled black circles), then on 2008-08-20 (filled red and blue circles; there are two measurements in the case of HD 14943). The positions predicted for the candidates on 2008-08-20 if they were background objects from the field are indicated by the empty red and blue circles, and their trajectories between the two epochs figured by the black curves, which take the stellar proper motions and the parallactic motions into account. The middle and lower panels show the evolutions of the projected separations and the position angles, respectively, with time. One-sigma error bars are represented. A zero or near-zero evolution of the separation and position angle with time indicates a physical association. The candidate at the left is bound to its star with indicative probabilities P_bkg = 0% and P_cmv = 96.7% (following the calculations of Sect. 4.2), while the candidate at the right is a background contaminant, with P_bkg = 12.0% and P_cmv = 0%.