The Beijing Electron Spectrometer III (BESIII) is a multipurpose detector
operating on the Beijing Electron Positron Collider II (BEPCII). After more
than ten year's operation, the efficiency of the inner layers of the Main Drift
Chamber (MDC) decreased significantly. To solve this issue, the BESIII
collaboration is planning to replace the inner part of the MDC with three
layers of Cylindrical triple-Gas Electron Multipliers (CGEM).
The new features of the CGEM detector will improve the spatial resolution to
130 μm. To meet this goal, a careful calibration of the detector is
necessary to fully exploit the potential of the CGEM detector. In all the
calibrations, the detector alignment plays an important role to improve the
detector precision. The track-based alignment for the CGEM detector with the
Millepede algorithm is implemented to reduce the uncertainties of the hit
position measurement. Using the cosmic-ray data taken in 2020 with the two
layers setup, the displacement of the outer layer with respect to the inner
layer is determined by a simultaneous fit applied to more than 160000 tracks. A
good alignment precision has been achieved that guarantees the design request
could be satisfied in the future. A further alignment will be performed using
the combined information of tracks from cosmic-ray and collisions after the
CGEM is installed into the BESIII detector