Position falsification attacks are one of the most dangerous internal attacks in vehicular networks. Several Machine Learning-based Misbehavior Detection Systems (ML-based MDSs) have recently been proposed to detect these attacks and mitigate their impact. However, existing ML-based MDSs require numerous features, which increases the computational time needed to detect attacks. In this context, this paper introduces a novel ML-based MDS for the early detection of position falsification attacks. Based only on received positions, our system provides real-time and accurate predictions. Our system is intensively trained and tested using a publicly available data set, while its validation is done by simulation. Six conventional classification algorithms are applied to estimate and construct the best model based on supervised learning. The results show that the proposed system can detect position falsification attacks with almost 100% accuracy.