## 1 Introduction  
The interactivity between real and virtual objects geometrically and temporally aligned in the real environment defines augmented reality (AR) [1]. The technological advances observed over the last decade have stimulated the implementation of several AR applications in industry [2; 3; 4; 5; 6; 7; 8]. The rigor of the precision and accuracy requirements for placing virtual elements in real environments combined with the progress achieved by devices in terms of these competencies has driven the development of AR solutions. Localization and tracking approaches in AR systems can be based on sensors, visual elements, or both [9]. Regardless of the approach used, factors such as the occlusion of markers, moving objects, noise, electromagnetism, and low light are often observed in industrial environments. They hinder or limit the ability to accurately determine the location and orientation of a device, adding tracking failures to an AR system [10]. Given these challenges, the ability to align virtual and real components with precision and accuracy can determine the feasibility of AR systems in industrial environments [9]. The common challenges inherent to this process include the reliability and scalability in the tracking of device movement [5; 10], calibration [2], and the precise contextualization of overlapping information in the real environment [10]. Some studies [11] use the recognition of fiducial markers as a strategy in augmented reality applications. However, execution environments are usually restricted to small spaces such as tables or workbenches. Therefore, they disregard or minimize the effects of factors that can negatively affect the experience of AR applications in an industrial environment. Although other studies [12] consider these aspects and cite the relevance of keeping the positioning of holograms precise and accurate as a precondition for standardized scientific experiments, they almost always present qualitative and subjective analyses of the precision and accuracy of the experiments. The literature describes the basic architectural components of AR systems: cameras, tracking systems, and user interfaces [5]. Although there are several ways to integrate these elements, studies highlight the relevance of head-mounted displays (HMDs) because they allow operators to move around and access information hands-free [5; 13]. Of the devices currently available in the market, the Microsoft HoloLens mixed reality device stands out in terms of performance, presenting itself as a complete and self-contained AR tool [14], i.e., an HMD with all the AR architectural elements embedded in a single device. These studies reveal the importance of representing holograms in AR applications with accuracy and precision, list the characteristics of industrial environments that hinder success, and, finally, reveal the demand for scientific productions that measure these parameters objectively. Thus, they contribute to the motivation of this study. Although it is possible to find a few studies, such as [15; 16], capable of proposing quantitative methods to measure the accuracy and precision of their AR solutions, the coverage area of the applications is limited to small distances (a few meters) and has low sampling. Considering the lack of studies related to the calibration of AR systems, specifically examining the challenges facing HoloLens observed in industrial environments in terms of applying AR solutions efficiently, the following question arises: how to develop a calibration method that helps AR systems to maintain the accuracy and precision of their solutions in industrial areas? To answer to that question, the objective of this study is to propose two models of 3D coordinate calibration for AR applications in an industrial indoor environment and compare these solutions' performances based on their accuracy and precision in displaying virtual objects in these scenarios. This study is divided into four sections including this introduction.