The knowledge of the states of a vehicle is a necessity to perform proper planning and control. These quantities are usually accessible through measurements. Control theory brings extremely useful methods -- observers -- to deal with quantities that cannot be directly measured or with noisy measurements. Classical observers are mathematically derived from models. In spite of their success, such as the Kalman filter, they show their limits when systems display high non-linearities, modeling errors, high uncertainties or difficult interactions with the environment (e.g. road contact). In this work, we present a method to build a learning-based observer able to outperform classical observing methods. We compare several neural network architectures and define the data generation procedure used to train them. The method is evaluated on a kinematic bicycle model which allows to easily generate data for training and testing. This model is also used in an Extended Kalman Filter (EKF) for comparison of the learning-based observer with a state of the art model-based observer. The results prove the interest of our approach and pave the way for future improvements of the technique.