As cities grow, efficient public transport systems are becoming increasingly important. To offer a more efficient service, public transport providers use systems that predict arrival times of buses, trains and similar vehicles, and present this information to the general public. The accuracy and reliability of these predictions are paramount, since many people depend on them, and erroneous predictions reflect badly on the public transport provider. When public transport vehicles move throughout the cities, they create motion patterns, which describe how their positions change over time. This thesis proposes a way of modeling their motion patterns using Gaussian processes, and investigates whether it is possible to predict the arrival times of public transport buses in Linköping based on their motion patterns. The results are evaluated by comparing the accuracy of the model with a simple baseline model and a recurrent neural network (RNN), and the results show that the proposed model achieves superior performance to that of an RNN trained on the same amounts of data, with excellent explainability and quantifiable uncertainty. However, an RNN is capable of training on much more data than the proposed model in the same amount of time, so in a scenario with large amounts of data the RNN outperforms the proposed model.