Human-robot interaction based on real-time kinematics or electromyography (EMG) feedback improves rehabilitation using assist-as-needed strategies. Muscle forces are expected to provide even more comprehensive information than EMG to control these assistive rehabilitation devices. Measuring in vivo muscle force is challenging, leading to the development of numerical methods to estimate them. Due to their high computational cost, forward dynamics-based optimization algorithms were not viable for real-time estimation until recently. To achieve muscle forces estimation in real time, a moving horizon estimator (MHE) algorithm was used to track experimental biosignals. Two participants were equipped with EMG sensors and skin markers that were streamed in real time and used as targets for the MHE. The upper-limb musculoskeletal (MSK) model was composed of 10 degrees-of-freedom actuated by 31 muscles. The MHE relies on a series of overlapping trajectory optimization subproblems of which the following parameters have been adjusted: the fixed duration and the frame to export. We based this adjustment on the estimation delay, the muscle saturation, the joint kinematic mean power frequency, and errors to experimental data. Our algorithm provided consistent estimates of muscle forces and kinematics with visual feedback at 30 Hz with a 110 ms delay. This method is promising to guide rehabilitation and enrich assistive device control laws with personalized force estimations.