The alignment of high-energy laser beams for potential fusion experiments demands high precision and accuracy by the underlying positioning algorithms whether it be for actuator control or for monitoring the beam line for potential anomalies. The feasibility of employing on-line optimal position estimators in the form of model-based processors to achieve the desired results is examined. We discuss the modeling, the development, the implementation, and the processing of model-based processors applied to both simulated and actual beamline data.