Humanoid robots are resourceful platforms and can be used in diverse application scenarios. However, their high number of degrees of freedom (i.e., moving arms, head and eyes) deteriorates the precision of eye-hand coordination. A good kinematic calibration is often difficult to achieve, due to several factors, e.g., unmodeled deformations of the structure or backlash in the actuators. This is particularly challenging for very complex robots such as the iCub humanoid robot, which has 12 degrees of freedom and cable-driven actuation in the serial chain from the eyes to the hand. The exploitation of real-time robot sensing is of paramount importance to increase the accuracy of the coordination, for example, to realize precise grasping and manipulation tasks. In this code paper, we propose an online and markerless solution to the eye-hand kinematic calibration of the iCub humanoid robot. We have implemented a sequential Monte Carlo algorithm estimating kinematic calibration parameters (joint offsets) which improve the eye-hand coordination based on the proprioception and vision sensing of the robot. We have shown the usefulness of the developed code and its accuracy on simulation and real-world scenarios. The code is written in C++ and CUDA, where we exploit the GPU to increase the speed of the method. The code is made available online along with a Dataset for testing purposes.