Real-time velocity estimation is a core task in autonomous driving, which is carried out based on available raw sensors such as wheel odometry and motor currents. When the system dynamics and observations can be modeled together as a fully known linear Gaussian state space (SS) model, the celebrated Kalman filter (KF) is a low complexity optimal solution. However, both linearity of the underlying SS model and accurate knowledge of it are often not encountered in practice. This work proposes to estimate the velocity using a hybrid data-driven (DD) implementation of the KF for non-linear systems, coined KalmanNet. KalmanNet integrates a compact recurrent neural network in the flow of the classical KF, retaining low computational complexity, high data efficiency, and interpretability, while enabling operation in non-linear SS models with partial information. We apply KalmanNet on an autonomous racing car as part of the Formula Student (FS) Driverless competition. Our results demonstrate the ability of KalmanNet to outperform a state-of-the-art implementation of the KF that uses a postulated SS model, while being applicable on the vehicle control unit used by the car.