Transverse mode instability (TMI) represents the main limitation for the power scaling of fiber laser systems with a diffraction-limited beam quality. In this context, it has become increasingly important to find a cheap and reliable way to monitor and characterize TMI and distinguish this effect from other dynamic perturbations. In this work, with the help of a position-sensitive detector, a novel method is developed to characterize the TMI dynamics even in the presence of power fluctuations. The position information of the fluctuating beam is recorded in the X- and Y-axis of the detector, which are used to track the temporal evolution of the center of gravity of the beam. The trajectories described by the beam within a specific time window contain rich information about TMI, which can be used to gain further insight into this phenomenon.