For travelling from point A to point B, autonomous vehicles generate a route between the points. During the mission, the vehicle uses a motion planning and controls algorithm to follow the planned route while avoiding static and dynamic obstacles. Motion planning algorithms generally plan over a future time horizon to smoothly follow the route and determine the car's optimal control (steering/acceleration). For planning through a future horizon, one requires the possible positions of all the relevant obstacles in future time-steps. Solutions for predicting an obstacle's future trajectory usually involve neural networks to perform sequence learning and generative algorithms to create multiple possibilities for a pedestrian's future state. This is done by attempting to learn the underlying distribution describing the obstacle motion. However, in practice, one cannot evaluate if this learnt distribution is accurate. This thesis addresses this issue by introducing a fully data-based alternative for trajectory prediction called the Partitioned Experience Method (PEM), which predicts future trajectories based solely on previously recorded data. In this way, it is not necessary to explicitly learn the underlying distribution of the pedestrian motion. The implemented trajectory prediction is validated using two metrics, recall and variance, introduced in this work. The trajectory prediction is also evaluated using a state-of-the-art motion planning algorithm. The results obtained from the motion planner indicate that using the PEM reduces the number of collisions and close contacts with other road users, and the corresponding trajectory followed by the car is closer to the reference trajectory.