The joint estimation of the state of charge (SoC) and the parameters of a battery model is typically done using nonlinear extensions of the Kalman filter (KF), such as the well-known and widely used extended KF (EKF), in combination with a simple but relatively accurate equivalent-circuit model. The main limitation of the joint EKF is that extensive tuning of the covariance matrices is required when implementing the observer in an application. This tuning is a tedious task with no clear guidelines for the tuning procedure. Furthermore, the joint EKF and its extensions do not explicitly address model uncertainty and sensor noise, which may be the cause for the problematic tuning. In this article, we combine a nonlinear observer with the structured representation of model uncertainty and disturbances as typically used in a robust-observer design approach. Therefore, the joint EKF for simultaneous estimation of SoC and model parameters will be presented for the case that includes cross-correlated noises. Moreover, inspired by the conditions for enforcing convergence of the SoC estimation error, a so-called forgetting factor will be introduced to the joint EKF. These adaptations lead to an observer with a single tuning parameter. The experimental results show that tuning of the proposed observer is straightforward and the performance is similar to a regular joint EKF with a root-mean-square SoC error of 0.5%.