The Giant Magellan Telescope (GMT) will place seven primary mirror segments of 8.4 m diameter on a common mount to form a single co-phased aperture of 25 m. 1High order adaptive optics (AO) using an adaptive secondary mirror that is segmented in the same way as the primary will correct the telescope's imaging to the diffraction limit in the near infrared. 2Critical to the performance of the telescope will be real-time correction of atmospherically-induced optical path differences between the primary mirror segments. Measuring these errors is challenging because of the large gaps between the segments, where the aberrated wavefront is not explicitly measured by the AO sensors, which are approximately 30 cm even at their narrowest points. In this paper we show that it will be feasible to estimate the path differences between the segments from the commands sent to the adaptive secondary mirror while the AO is running in closed loop. These commands will be an approximate representation of the open-loop atmospheric wavefronts. We have investigated the value of the approach with real-time closed-loop deformable mirror command data from the first-light AO system now running on the Large Binocular Telescope (LBT). 3,4The data are of very high quality and realistically capture the spatio-temporal behavior of the wavefront. We use data from two nights to show that the GMT segment pathlength errors may be recovered to <25 nm accuracy with a simple linear estimator. Additional simulations show similar performance, which, with high-order AO, is quite adequate to maintain high Strehl ratio at near infrared wavelengths.