## 2 Background
### AR Placement Methods: Related Works  
Several developments in AR have been carried out with or without markers (sensor-based or computer vision) to address and evaluate the challenges of an AR system in terms of visualization, portability, placement, etc. Ref. [53] defined the nature and sensitivity of the errors that cause misregistration in AR displays (in the case of a head-mounted display). They consist of system delay (latency), tracker error, calibration error, optical distortion, model misalignment, etc. However, neither on the screen nor in the world coordinate systems does this research provide a model for estimating the overall error of the AR system. Ref. [54] studied the camera's theoretical pinhole model's ability to accurately represent virtual objects on the screen. The authors measured pixel errors on the screen to assess the impact of the camera in the AR context but did not evaluate the variances of their representation in the real scene in world coordinates (real scale distances). Ref. [20] addressed the placement problem by showing that the alignment of virtual objects with the real world can be performed by aligning the real and virtual cameras. To obtain a coherent augmented world combining both virtuality and reality, it is necessary to attribute to the virtual camera the same properties (extrinsic and intrinsic) as those of the real camera and to determine in real time for each image the position and the orientation of the camera in the real scene. An overview of AR application in underground constructions was presented by [55] who addressed both aspects: 3D modeling and AR placement or alignment. The purpose of this study was to give a comprehensive overview of the literature on the application of AR in the building field. The authors identified and examined the challenges, as well as the technical approaches, to solve fundamental barriers to technology adoption in the underground construction industry. They emphasized virtual object placement and alignment issues, as well as related errors. In the same trend, Ref. [19] investigated the placement accuracy of an AR system for underground utility mapping in an outdoor environment. They tested if a smartphone linked to an external GNSS receiver might help to improve and assess horizontal positional inaccuracies in collected data. The data were collected using a phone app called \"AR XR-GIS\". The study evaluated four devices with 16 location points using root-mean-square error (RMSE), mean Euclidean error (MEE), and central error (CE). However, a study conducted by [PERSON] et al. (2018) has shown a smartphone positioning accuracy of around 0.80 m to 1.4 m. Thus, existing smartphones cannot be used in underground construction without the addition of higher-accuracy GNSS devices [56]. Ref. [13] proposed a methodology to evaluate AR placement errors. The main objective of their study was to present a reproducible methodology for calculating the real distances between any real point and the lines of sight of its virtual projections to obtain a quantitative evaluation of these superimposed deviations for any AR application. The authors indicated that there are several possible sources of errors, which do not allow obtaining a perfect superposition of the virtual models on their corresponding real entities. The results were synthesized according to the factors of influence (the AR Scene, geolocation, orientation and camera alteration), the methodology of contrast and evaluation, the partial precision and the corrective actions. For the case of geolocation (placement by GNSS), it was mentioned that it is possible to obtain precise results in X and Y coordinates which do not affect the general precision of the system when the application is not used over very short distances. This was indicated by moving the external GNSS receiver up to 5 cm and checking that the overlay was the same.