Mapping an environment with a Light Detection and Ranging (LiDAR) sensor through the use of a LiDAR Simultaneous Localization And Mapping (SLAM) algorithm is a powerful technology that allows for the creation of detailed 3D models. Recently various LiDAR sensors have been developed based on Micro-Electro-Mechanical System (MEMS) technology. These LiDARs are very low cost and considerably smaller than conventional LiDARs. They also often incorporate other sensors such as Inertial Measurement Unit (IMU)s and cameras into the same device. Performing LiDAR SLAM with MEMS based LiDAR is challenging due to the short range, the smaller Field of View (FOV) and the sensitivity to ambient light of MEMS based LiDAR. In this thesis the objective is to reduce the effect of these factors when doing LiDAR SLAM by incorporating IMU measurements into the position estimation of the sensor. A graph based positioning approach is proposed to achieve tight coupling of the IMU sensor and LiDAR position estimates. The method is made more robust by incorporating an outlier detection mechanism that reduces the influence of wrong LiDAR position estimates caused by insufficient points in the LiDAR FOV or by ambient light disturbance. The method was built in ROS and implemented on the Intel ® L515 sensor. The performance is evaluated in indoor situations with varying presence of ambient sunlight and where room size approaches the maximum limit of the sensor range. The algorithm achieves lower drift than the current state of the art for the Intel ® L515. The algorithm especially achieves altitude drift reduction and increases robustness to outliers in the LiDAR positioning.