The extrinsic calibration of a Mobile Laser Scanning system aims to determine the relative orientation between a laser scanner and a sensor that estimates the exterior orientation of the sensor system. The relative orientation is one component that limits the accuracy of a 3D point cloud which is captured with a Mobile Laser Scanning system. The most efficient way to determine the relative orientation of a Mobile Laser Scanning system is using a self-calibration approach as this avoids the need to perform an additional calibration beforehand. Instead, the system can be calibrated automatically during data acquisition. The entropy-based self-calibration fits into this category and is utilized in this contribution. In this contribution, we analyze the impact of four different trajectories on the result of the entropy-based self-calibration, namely (i) uni-directional, (ii) ortho-directional, (iii) bi-directional, and (iv) multi-directional trajectory. Theoretical considerations are supported by experiments performed with the publicly available <i>MLS 1 – TUM City Campus</i> data set. The investigations show that strong variations of the yaw angle in a confined space or bidirectional trajectories as well as the variation of the height of the laser scanner are beneficial for calibration.