In manufacturing tasks with industrial robots, such as grinding, force control is essential for achieving results comparable to those of conventional machine tools. The current state of the art relies on force-torque sensors mounted between the robot wrist and the end effector, which come with drawbacks such as higher costs and increased integration effort. Ongoing research aims to replace these sensors by estimating the process force using disturbance observers. This paper focuses on improving estimation performance by employing a moving horizon estimator, which enhances accuracy by generating state estimates through optimization-based fitting of measurement data from a specific time window into a modeled representation of the system dynamics. The analysis is conducted using a test bench that represents a high-payload industrial robot joint. The results demonstrate that, compared to unscented Kalman filters, moving horizon estimation improves bandwidth and disturbance rejection during estimation while maintaining real-time capability.