The precise overlay in see-through AR applications and the development of methods to calculate the registration error for such applications using an AR head-mounted display (HMD) present significant challenges. This difficulty arises primarily due to the absence of ground truth data (GTD) as the scene is partially hidden by view restrictions. Traditional approaches may require expensive setups, like cameras or laser scanners, to capture the hidden area and generate GTD. We propose an approach to calculate the registration error by using a marker-based pose estimation method. We use synthetic data to show the suitability of our method. The synthetic data is created in Unity, where we replicated a see-through application. Therefore, we employ image augmentation technologies for simulating a real see-through forklift application. The utilization of the simulation environment enables the generation of GT). This data forms the basis for evaluating the accuracy of our proposed method. Our primary contributions include a simulated see-through AR application in Unity, a labeled, application-specific synthetic dataset, and a validated method for determining the 3D registration error in world units (mm). This work demonstrates the suitability of the development of a marker-based registration error method to determine a 3D registration error in AR HMD see-through applications, providing an alternative to traditional, more costly approaches.