## 4 Discussions  
Imposed 1D, 2D, and 3D movements were estimated from baseline vectors only to show the differences from the true movements in a case where adjustment of the geodetic network is not carried out (Figure 5). The MAE of 2D displacements is in the range of 1.0-1.7 mm; for 3D displacements, the MAE is in the range of 1.3-2.5 mm, while the value of MAE is greater for 1D displacements, ranging from 1.9 to 3.3 mm (Table 4). However, the differences between MAE of used antennas are at the millimeter level or even smaller. To increase the accuracy of estimated displacements, the geodetic adjustment of the network was carried out, where the data were defined by three points of the geodetic network that did not have movements between sessions. The a posteriori standard deviations were estimated (Tables 5 and 6) for sessions when vertical and horizontal movements were imposed. With a significance level of 5%, we could not reject the null hypothesis, and homogenous network precision was obtained in all combinations between sessions. The a posteriori standard deviation is in the range of 0.9-2.3 mm for all sessions. The results from Tables 5 and 6 show that using the Survey Calibrated antenna, where antenna calibration parameters are known, results in higher precision of estimated positions. The improvement may be as much as 50%. However, the differences are in the order of millimeters or even smaller. Vertical movements were imposed in steps of 3 mm and ranged from 3 to 15 mm, and horizontal movements were in steps of 2 mm and ranged from 2 to 12 mm. For 1D displacement detection, we were not able to detect 3 mm with statistical significance (more than 95%) with any of the used antennas in combination with the ZED-P9P GNSS chip (Table 7). Displacements were detected in 60%, 20%, and 20% of cases for Survey Calibrated, Survey, and Tallysman antenna, respectively. The Survey Calibrated antenna can detect 6 mm displacements; however, this does not hold true for Survey and Tallysman antennas (only 75%). Displacements with a size of 9 mm were detected (100%) with all three GNSS antennas. Horizontal displacements were imposed in steps of 2 mm. Based on the results presented in Table 8, it can be concluded that 2 mm displacements cannot be detected by low-cost GNSS instruments. The Survey Calibrated and the Tallysman antennas were able to detect 4 mm displacements, while the Survey antenna did not. Horizontal displacements of 6 mm or larger could be detected (100%) by the three used GNSS devices. In monitoring natural objects and man-made structures, movements can occur in any direction (spatially), so we estimated the imposed horizontal movements in a 3D coordinate system. From the results presented in Table 9, we can conclude that 6 mm displacements can be detected by all antennas, while a low percentage (60%) of 4 mm displacements were detected with the Survey antenna. The smallest imposed movements (2 mm) were not detected by low-cost GNSS instruments. Only 17% of considered displacements of the magnitude 2 mm were detected. The results presented in Tables 7-9 indicate that the Survey Calibrated antenna had better positioning performance. The Survey Calibrated antenna outperformed the others in terms of the sizes of detected 1D, 2D, and 3D movements. The Tallysman antenna was better than the Survey antenna in detecting 2D and 3D movements, while they provided the same results when detecting 1D movements. Neither antenna performed as well as the Survey Calibrated antenna. Horizontal and vertical movements were imposed by a special mechanism with high accuracy. Therefore, the true values of displacements are well known. The MAE values with respect to the true values were estimated for all displacements (Table 10). The Survey Calibrated antenna has a smaller MAE (0.9 mm) of 1D displacements than both uncalibrated antennas. For the Survey and Tallysman antennas, the MAE values are 1.2 mm, and 1.3 mm, respectively.