Track-based alignment for the BESIII CGEM detector in the cosmic-ray test

The Beijing Electron Spectrometer III (BESIII) is a multipurpose detector operating on the Positron Collider II (BEPCII). After more than ten year's operation, efficiency of inner layers Main Drift Chamber (MDC) decreased significantly. To solve this issue, BESIII collaboration planning to replace part MDC with three Cylindrical triple Gas Multipliers (CGEM). transverse plane spatial resolution CGEM required be 120 $\mu$m or better. meet goal, careful calibration necessary fully exploit potential detector. In all calibrations, alignment plays an important role improve precision. track-based for Millepede algorithm implemented reduce uncertainties hit position measurement. Using cosmic-ray data taken in 2020 two setup, displacement and rotation outer layer respect determined by simultaneous fit applied 160000 tracks. A good precision has been achieved that guarantees design request could satisfied future. further going performed using combined information tracks from collisions after installed into