## 3 Materials and Methods  
### Measurement System  
The underlying principle of the RTK GNSS-assisted terrestrial SfM photogrammetry method is to record camera positions with a centimeter accuracy. Accurately knowing these (X, Y, Z) coordinates simplifies the collinearity equations by removing unknowns, which do not need to be solved during bundle block adjustment while using GCPs. Using this approach, the camera orientation is not a priori measured, but estimated with tie points during bundle block adjustment. To record the camera position with sufficient accuracy, we developed a measurement system (Figure 2) that is composed of (i) a light tripod for photography, (ii) a custom-built wood frame, (iii) a camera (Reflex camera or Smartphone), and (iv) the mobile antenna and pad of a RTK GNSS. The wood frame is used to mechanically connect the mobile antenna of the RTK GNSS receiver and the camera. Figure 1: (**a**) Localization of the study area of Porsmilin beach at the entrance of the Bay of Brest in Brittany (France). (**b**) Orthophotograph of Porsmilin beach (computed from drone images). (**c**) Western cliff. For this study, we used a Topcon(r) HiPer V GNSS receiver. The GNSS base station is set up on an existing geodetic marker located near the car park at the north-east of the study site (see Figure 1b). The same GNSS base was used for both the RTK GNSS-assisted terrestrial SfM photogrammetric survey and validation surveys. We tested the method with a Nikon D800 Reflex camera (with a focal length of 20 mm) and with a Huawei Y5 (2016) Smartphone camera (with a focal length of 4 mm). Table 1 summarizes the characteristics of the photographs taken with both sensors. All of the images were taken in landscape format, as it represents the easiest way to mount the camera on the tripod, also allowing for maximizing the spatial coverage for a given overlap. The wood frame was designed so that the GNSS antenna and the camera center are vertically aligned. This configuration facilitates the pre-processing of data, since it limits the offset between the camera perspective center and the GNSS antenna phase center to a vertical component. Using this configuration, several images can be obtained from the same position by spinning the camera around this vertical axis, without moving the tripod. More particularly, having no horizontal offset between the camera and the GNSS antenna avoids having to determine the eccentricity vector for each shot and, hence, to determine the azimuth of the horizontal shift between the GNSS antenna phase center and the camera perspective center. As the GNSS receiver is used to measure the camera position, not the ground topography, it is not necessary to measure or to keep constant the height of the camera above the ground. Indeed, as the distance (noted D) between the camera and the GNSS antenna is kept constant throughout all image acquisitions, this offset is directly subtracted from the position that is measured by the GNSS antenna (Equation (1)), providing accurate camera location. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Camera Model** & **Reflex Camera—Nikon D800** & **Smartphone—Huawei Y5 2016** \\ \hline
**Focal Length** & 20 mm & 4 mm \\
**Image Size** & \(3680\times 2456\) pixels (9 Mpix) & \(3264\times 1840\) pixels (6 Mpix) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Characteristics of the images taken by the Reflex camera and the Smartphone camera. Figure 2: Measurement system developed for the Real Time Kinematic (RTK) Global Navigation Satellite System (GNSS)-assisted terrestrial Structure-from-Motion (SfM) photogrammetry method (equipped with the Nikon D800 Reflex camera or with the Huawei Y5 Smartphone). \[\left( \begin{array}{c}X_{Cam}\\ Y_{Cam}\\ Z_{Cam}\end{array} \right)=\left( \begin{array}{c}X_{\text{GNSS}}\\ Y_{\text{GNSS}}\\ Z_{\text{GNSS}}\end{array} \right)-\left( \begin{array}{c}0\\ 0\\ 0\\ D\end{array}