Roboy 3.0 is an open-source tendon-driven humanoid robot that mimics the musculoskeletal system of the human body. Roboy 3.0 is being developed as a remote robotic body - or a robotic avatar - for humans to achieve remote physical presence. Artificial muscles and tendons allow it to closely resemble human morphology with 3-DoF neck, shoulders and wrists. Roboy 3.0 3-DoF joints are implemented as ball-and-socket joints. While industry provides a clear solution for 1-DoF joint pose sensing, it is not the case for the ball-and-socket joint type. In this paper we present a custom solution to estimate the pose of a ball-and-socket joint. We embed an array of magnets into the ball and an array of 3D magnetic sensors into the socket. We then, based on the changes in the magnetic field as the joint rotates, are able to estimate the orientation of the joint. We evaluate the performance of two neural network approaches using the LSTM and Bayesian-filter like DVBF. Results show that in order to achieve the same mean square error (MSE) DVBFs require significantly more time training and hyperparameter tuning compared to LSTMs, while DVBF cope with sensor noise better. Both methods are capable of real-time joint pose estimation at 37 Hz with MSE of around 0.03 rad for all three degrees of freedom combined. The LSTM model is deployed and used for joint pose estimation of Roboy 3.0's shoulder and neck joints. The software implementation and PCB designs are open-sourced under https://github.com/Roboy/ball_and_socket_estimator