We study overconstrained polynomial systems from an algebraic and numerical perspective in order to improve the accuracy and reliability of Gough platform calibration. By elimination theory, we may limit ourselves to measuring only the position information by external sensors, besides internal sensor measurements. Measuring orientation, which is intricate and error-prone, becomes unnecessary. A planar analogue is used to formally develop the technique and analyze observability by means of the Jacobian. Several experiments are used to compare the existing alternatives with partial information to our approach, by numerical simulation. It is shown that our method significantly improves robustness without compromising accuracy, especially when the measured configurations lie at the workspace's boundary.