Statistical comparison analysis of different real-time kinematic methods for the development of photogrammetric products: CORS-RTK, CORS-RTK + PPK, RTK-DRTK2, and RTK + DRTK2 + GCP

Abbreviations

ANOVA

analysis of variance

CORS

continuously operating reference station

CPs

check points

DEM

digital elevation models

DJI

Dà-Jiāng Innovations

DRTK2

dynamic real-time kinematic 2

DTMs

digital terrain models

GCPs

ground control points

GGM10

Gravimetric Geoid of Mexico 2010

GNSS

global navigation satellite system

GS

ground station

GSD

ground sample distance

INEGI

National Institute of Statistics and Geography

LAN

local area network

LIDAR

laser imaging detection and ranging

LSD

least significant difference

NTRIP

networked transport of RTCM via internet protocol

PPK

post-processed kinematic

PPP

precise point positioning

RGNA

active national geodetic network

RMSE

root mean square error

RTCM

radio technical commission for maritime services

RTK

real-time kinematic

UAV

unmanned aerial vehicle

UTM

Universal Transverse Mercator

1 Introduction

In the last decade, digital photogrammetry technology has progressed rapidly with the use of unmanned aerial vehicles (UAVs) because of the large number of sensors and devices that can be adapted to them to obtain data with higher spatial, spectral, temporal, angular, and radiometric resolution, reducing cost, time, and human resources. Photogrammetry with UAVs has been used for the development of several studies such as topographic surveys [1,2], characterization of vegetation structure [3,4], implementation of precision agriculture to improve farmland management, increasing crop yields [5,6], 3D modeling and visualization of archaeological structures [7,8], inspection of buildings and dams [9,10,11], identification of changes in urban and rural landholdings in cadastral studies [12], spatiotemporal monitoring of changes derived from natural phenomena and anthropogenic activities [13,14], detection of geomorphological changes in rivers [15], and the characterization of ice, glacial, and peri-glacial morphology [16,17].

In topography, digital elevation models (DEM) and ortho-photographs are the main results of photogrammetric processing of images obtained with UAVs, where the altimetric and planimetric accuracy represent the most relevant concerns of these products [17,18,19,20] since they are directly related to particular scientific and professional purposes. Normally, the georeferencing of photogrammetric models has been performed indirectly, establishing ground control points (GCPs) on the study surface, but this task is labor-intensive, time-consuming, and costly. However, the direct georeferencing of these models has been in constant evolution due to the technology integrated into UAVs.

Global navigation satellite systems (GNSSs) are used for UAV positioning. However, a GNSS signal blockage or a malfunction could damage the navigation system, especially if it relies exclusively on GNSS. To achieve redundancy, integrated navigation systems have been developed to ensure reliability, availability, and reliable autonomous navigation. Real-time kinematic (RTK) and post processed kinematic (PPK) technologies are significant steps in the evolution of digital aerial photogrammetry with UAVs. RTK is a crucial tool for real-time positioning in surveying and other applications that demand high levels of accuracy [21,22]. This technique uses a GNSS receiver as a reference station at a known coordinate, which then sends correction information to rover receiver(s) via an ultra-high frequency radio modem. PPK is another type of correction technology like RTK but corrects the location data after they are collected and uploaded. Both RTK and PPK technologies can achieve positioning accuracy ranging from a few centimeters to 0.1 m near the base station and are used to obtain precise location data as a substitute for conventional methods, such as GCPs [23].

Nowadays, the use of networked transport of RTCM via internet protocol (NTRIP) and continuously operating reference stations (CORS) for RTK correction is of great significance for the development of photogrammetric products. NTRIP enables the transmission of RTK correction data via the internet, supporting real-time positioning with high accuracy. Therefore, the need for a direct communication link between the base and rover receivers is eliminated, reducing cost, and simplifying field operations [24]. On the other hand, CORS is a network of reference stations that continuously collects GNSS data at known locations. These reference stations provide accurate and up-to-date correction data for RTK positioning. By using CORS data, the accuracy of the RTK measurements can be improved, where signal blockages or malfunction limitations can be overcome [25]. The combination of NTRIP and CORS enhances the effectiveness of RTK correction by enabling wider coverage, reducing reliance on local base stations, and improving the availability and accuracy of correction data [26].

The studies evaluating the accuracy of data collected by UAVs are normally conducted using GCPs or check points (CPs) [27]. Few recent studies have been developed comparing different methods using the RTK approach. Taddia et al. [21] reported the use of the PPK method to generate photogrammetric models and digital terrain models (DTMs) of coastal areas by employing GNSS data from CORS with a Dà-Jiāng Innovation (DJI) Phantom 4 RTK drone. The results show that very similar accuracies were found with and without using GCPs. Zeybek [25] evaluated the performance of planimetric and altimetric accuracy in 24 flights by direct georeferencing (without GCP) varying flight heights between 75 and 100 m, using the CORS and the Dynamic RTK 2 (DRTK2) methods. The DRTK2 method consisted of using the DRTK2 GNSS receiver manufactured by the DJI-P4 RTK company (Phantom 4 RTK UAV) to provide centimeter-level positioning accuracy in RTK. According to Zeybek [25], both methods provided acceptable positional accuracy levels, with root mean squared error (RMSE) values of 0.01–0.03 m for the horizontal axis and 0.04–0.06 cm for the vertical axis.

Štroner et al. [28] reported the accuracy of horizontal and vertical coordinate components obtained using an RTK UAV system and GCPs with a DJI Phantom 4 RTK. The results demonstrated that the errors of the RTK UAV system were similar to those obtained with GCPs in horizontal coordinates, but the errors in vertical coordinates were 2–3 times greater. Eker et al. [29] compared UAV-based RTK and PPK methods for six different surface types (roads, shadows, shrubs, boulders, trees, and ground). The lowest RMSE was observed on a solid textured surface since the surface types of ground, roads, and shrubs showed an RMSE 0.10 m lower than that of other surface types.

Other studies have focused on determining the influence of external factors on the UAV RTK technology. Cho and Lee [30] observed an accuracy reduction caused by the lack of RTK signal and proposed the use of GCP and PPK to deal with RTK signal interruption in UAV photogrammetry. Tomaštík et al. [31] evaluated the effect of vegetation seasonal variation on the accuracy of photogrammetric products (point cloud, orthoimages, and DEMs). The results evidenced that the UAV RTK/PPK technology was not influenced by vegetation seasonal variation. Kefauver et al. [32] assessed the effect of different flight patterns and altitudes on positional accuracy. They demonstrated that it is possible to enhance positioning accuracy when real-time positional access is combined with post-processing techniques. Martínez-Carricondo et al. [33] demonstrated that using multiple fixed GNSS base stations simultaneously can reduce the systematic error of elevation data for RTK photogrammetric processes, improving altimetric accuracy without the need to use GCPs or oblique photographs.

Despite several studies that have been carried out to assess the accuracy of UAV georeferencing, most of these studies only evaluate the georeferencing methods separately and no fair comparison between these methods is given [32,34,35,36,37,38]. While some studies refuse the use of real-time positioning methods without the use of GCPs [39,40], other studies acknowledge the significance, potential, and effectiveness of the PPK method for UAS surveys [22,31,41,42,43]. Also, the precise point positioning (PPP) method provides real-time positioning using corrections from multiple reference stations to compute precise satellite orbits and clock errors, achieving high-precision positioning without relying on nearby base stations [44,45,46]. However, the PPP method was not analyzed in this study.

The aim of the present work is to evaluate the altimetric and planimetric accuracy by comparing four different methods that are based on the RTK approach (CORS-RTK, CORS-RTK + PPK, RTK + DRTK2, and RTK + DRTK2 + GCP) using the same morphological conditions. 28 CPs obtained from GNSS antennas were used to assess the altimetric and planimetric accuracy for each method, but CPs 12 and 25 were eliminated because they were damaged before the photogrammetric flights were made. Once the performance of the altimetric and planimetric accuracy was obtained, a rigorous statistical analysis was carried out through ANOVA and the least square difference (LSD) multiple range test. These statistical analyses were used to demonstrate a statistically significant difference between different methods and to determine the method with the least error (greater accuracy). This statistical comparison has not been implemented in any previous work, which represents a novel scheme for the improvement of photogrammetric products using UAVs, such as DEM and ortho-photographs.

2 Methods

2.1 Study area

The study area was an urban area of the city of Culiacan, Mexico, which covers approximately 16 ha between coordinates 24.751554°, 24.746705° latitude, and −107.395484°, −107.392541° longitude (Figure 1). Part of the study area is urbanized, characterized by paved roads, buildings, and private households, but the presence of unpaved roads and vegetation is also distinguished. This area was selected because an elevation difference of 37 m is observed in the terrain. The presence of anthropogenic buildings and vegetation, and the variation in terrain elevation are external factors that could have an important effect on the accuracy of the RTK techniques used in this study.

Figure 1

Study area.

2.3 Methodology

The methodology used in the present study was carried out in five stages. Stage 1 consisted of establishing a network of CPs distributed strategically throughout the study area. These CPs cover the entire area and were located in a network of irregular triangles with angles of approximately 60° as suggested by Zhang et al. [47]. These points were not obstructed by any vertical structure or vegetation shadow (Figure 2). The maximum distance between the CP points was approximately 150 m since the positioning of these points was based on topography and surface configuration. CPs were only used to verify the accuracy of the photogrammetric products obtained and did not intervene in the digital photogrammetric processing. In turn, GCPs are used to adjust the orientation of the images during photogrammetric processing. However, both (CP and GCP) are measured and established with the same methodological rigor.

Figure 2

Distribution of the CP network.

Some points of this CP network were established on concrete sidewalks or other types of concrete structures. Other points were on the natural terrain. In these cases, a flat concreted structure was constructed with dimensions of 0.40 m × 0.40 m (Figure 3a). A red mark was rendered in these structures throughout the CP network (Figure 3b and c). This rendering was carried out to facilitate the identification of CPs in the images acquired by the drone.

Figure 3

Establishment and measurement of CP marks. (a) Flat concreted structure was constructed with dimensions of 0.40 m × 0.40 m; (b and c) red mark was rendered in these structures throughout the CP network; (d) Measuring CPs with the mobile antenna in RTK mode.

In stage 2, a GNSS base point was established. This point was measured with a GNSS receiver model CHC x900 at intervals of 5 s for 2.5 h. The information acquired was processed and adjusted with the active national geodetic network (RGNA) of Mexico using the monitoring station called “CULC” located in the center of the city of Culiacan and at an approximate distance of 5.3 km from the present study area. The RGNA is operated by the National Institute of Statistics and Geography. After, the GNSS base receiver was installed and kept on a known point (GNSS base point), the mobile antenna in RTK mode was used to obtain the coordinates of each CP throughout the CP network. A bipod was set up at each point of interest to ensure the receiver was positioned correctly (centered and leveled) (Figure 3d). This procedure was carried out to ensure accurate and reliable measurements minimizing errors caused by uneven ground.

Stage 3 consisted of defining the photogrammetric flight parameters and the type of photogrammetric survey [48,49]. Two flights were performed at an altitude of 70 m. Under this condition, the ground sample distance (GSD) is comparable with the accuracies obtained with GNSS antennas in RTK mode. The DJI GS RTK App was used to plan the RTK flight. To produce accurate aerial maps, this software automatically determined the photogrammetric parameters as a function of the flight height and the longitudinal and transverse overlaps. In this study, a flight speed of 5 m/s was used, with a camera angle of −90°, a forward overlap of 80% and a side overlap of 70% according to the suggestion by Mora-Felix et al. [20].

The photogrammetric flight 1 was processed using two different approaches: RTK-CORS and RTK-CORS + PPK. The RTK-CORS approach was based on the NTRIP protocol, where a rover receiver was connected to a reference station (CORS) via the internet. The CORS station collected the receiver’s data from multiple GNSS satellites, calculated the positioning information, and generated the correction data based on the difference between the measured and known positions. These correction data were sent to the rover receiver through the NTRIP protocol. This enabled to achieve centimeter-level accuracy in positioning [25]. The approximate distance between the CORS station and the study area is 4.66 km.

In the RTK-CORS + PPK approach, the rover receiver collects real-time corrections from the nearest CORS station, similar to the RTK-CORS approach. Then, the raw GNSS data are compared with the precise data from the reference station in post-processing software called Redtoolbox [41] to calculate highly accurate positions. The post-processing consisted of adjusting the coordinates of each of the images, taking into account factors such as atmospheric conditions and satellite orbits that could affect real-time positioning [50].

The photogrammetric flight 2 was also processed using two different approaches: RTK + DRTK2 and RTK + DRTK2 + GCP. RTK + DRTK2 combines RTK positioning with advanced algorithms and technologies to enhance the accuracy and reliability of real-time positioning for UAVs. The DRTK2 technology was developed by DJI enterprise and designed specifically for UAV applications [51]. This system consists of a mobile ground station called DRTK2, which is an enhanced GNSS receiver antenna that provides real-time differential corrections to the moving UAV that can communicate via 4G, OcuSync, WiFi, and LAN, ensuring stable and continuous data transmission. Therefore, high accuracy and precision in positioning while in flight can be achieved even in difficult environments with obstacles or interference [52].

The RTK + DRTK2 + GCP approach was based on the RTK + DRTK2 method, where the RTK base station, rover receiver, and DRTK 2 mobile station work together to achieve highly accurate real-time positioning for the drone. By using this technology, the drone captures aerial imagery, and the collected data were processed using Agisoft Metashape Professional software. During the photogrammetric process, some of the CPs were used as reference points to accurately align and georeference the captured data. The alignment and georeferencing process was carried out using six CPs as GCPs. These GCPs were CP1, CP9, CP15, CP18, CP22, and CP27 (Figure 2).

In stage 4, all photogrammetric processes were performed in Agisoft Metashape Professional software using a standard workflow. First, the UAV images were imported from the files to the software. Then, the projection of Geodetic coordinates was changed to Universal Transverse Mercator Zone 13 North (UTM 13N) and the vertical coordinate reference system GGM10 (Gravimetric Geoid of Mexico 2010), because the CORS antenna is referenced to this vertical coordinate reference system. A high-precision image orientation process was carried out using the reference values (40,000 key points per image and 4,000 link points per image). The adaptive model of camera adjustment was selected since the UAV camera already has a lens correction to reduce distortion errors. This procedure was performed for all photogrammetric processing modes, except for the RTK + DRTK2 + GCP method where six CPs were used as GCPs, as mentioned before. The dense point cloud was performed for each of the photogrammetric processes, using high-quality depth filtering, which eliminated areas with low stereo vision, and calculated the disparity for each pixel using the structure from motion multi-stereo vision algorithms [53]. The DEM was created using the dense point cloud and the orthophotography was generated from the DEM for each of the processes.

Stage 5 consisted of evaluating the planimetric and altimetric accuracy of the orthophotography and DEM results from the different photogrammetric processes. This evaluation refers to the proximity of the observation of a coordinate point to a true value. In this study, the true coordinates were obtained directly with the GNSS antennas (CPs). The true coordinates were compared with the coordinates obtained from the orthophotography and DEM according to the marks observed. The root mean square error (RMSE) was used to measure the difference between the values obtained from the orthophotography and DEM with the true coordinates (GNSS points) [20,54].

Equation (1) was used to validate the planimetric error (RMSE _X , _Y ), which was calculated as the distance between the GCPs and the marked points (CPs) on the ground in both the x and y coordinates [20].

(1) RMSE X , Y = ∑ i = 1 n ( ( ( X GNSS − X ORT ) 2 + ( Y GNSS − Y ORT ) 2 ) ) n ,

where X GNSS and Y GNSS are the X and Y coordinates measured with GNSS antennas; X ort and Y ort are the coordinates obtained from the orthophotography, respectively; and n is the number of points used for the accuracy assessment.

By using equation (2), the altimetric accuracy (RMSE _z ) of the DEM was assessed. RMSE _z compared the elevation points acquired through GNSS with those that were marked on the ground [20].

(2) RMSE Z = ∑ i = 1 n ( ( Z GNSS − Z DEM ) 2 ) n ,

where z GNSS is the Z coordinate of the GNSS antenna measurements; and Z DEM is the elevation coordinates obtained from the DEM.

The global error (RMSE _x,y,z ) was measured by using the RMSE in the three-dimensional coordinates (X, Y, and Z coordinates). This statistic represents the overall accuracy between the estimated values and the true values in all three spatial dimensions (equation (3)) [55].

(3) RMSE X , Y , Z = ∑ i = 1 n ( ( ( X GNSS − X ORT ) 2 + ( Y GNSS − Y ORT ) 2 + ( Z GNSS − Z DEM ) 2 ) ) n ,

where X GNSS , Y GNSS , and Z GNSS are the X, Y, and Z coordinates measured with GNSS antennas; and X ort , Y ort y Z DEM are the coordinates obtained from orthophotography and DEM.

An analysis of variance (ANOVA) was performed to evaluate whether any of the photogrammetric processing approaches influenced the accuracy of the photogrammetric products obtained (orthophotography and DEM). The planimetric and altimetric errors obtained were used as the response variable for this statistical analysis. A multiple-range test was used to determine significant differences between the different real-time positioning methods. This test was performed to identify the methods that are significantly different from each other. In this study, the LSD multiple range test was carried out once the ANOVA test indicated that significant differences were found between the methods. A significance level (α) of 0.05 was set for hypothesis testing in both ANOVA and LST statistical analyses since this is the most common value used for statistical decision-making.

3 Results

Since the photogrammetric products observed no visual difference between the different methods, this study only shows the orthophotographs and DEM obtained with the RTK-CORS + PPK method as an example of the photogrammetric processing (Figures 4 and 5). The pixel size was 2.2 cm × 2.2 cm (GSD size) in all orthophotographs and DEMs.

Figure 4

Orthophotograph obtained with the RTK-CORS + PPK method.

Figure 5

DEM obtained using the RTK-CORS + PPK approach.

Based on these photogrammetric products, the CP coordinates were extracted at the sub-pixel level from each of the different photogrammetric processes. The difference between the estimated and the measured coordinates was determined. These differences (errors) were obtained at each of the CPs for the different methods.

The RTK-CORS method showed the highest absolute errors, mainly in the elevation, where the maximum difference was 0.377 m at CP17 (Figure 6), and a mean elevation error of 0.156 m was observed, being this CP, the one with the greatest topographic unevenness and therefore the greatest distance between the drone at the moment of the image capture and the terrestrial surface. The planimetry error showed a slighter error variation, where a maximum difference of 0.071 m was observed in the X axis, while a maximum error of 0.024 m was observed in the Y axis. Figure 6 confirms that the RTK-CORS method presented the greatest error variation. In particular, the greatest error difference in the Z coordinate was found from CP9 to CP27, because these points present a significant topographic unevenness with respect to the drone takeoff point. Therefore, the RTK-CORS method was the most sensitive approach since slight changes in photo scale (terrain elevation variation) produced the greatest errors. In this method, the greater the distance between the sensor and the photographed surface, the greater the error was observed.

Figure 6

Errors in the Z axis for each method evaluated.

The RTK-CORS + PPK method presented the lowest error difference in planimetry. This method showed maximum differences of 0.026 m on the X-axis and 0.027 m on the Y-axis. These values are lower than those observed for the other real-time positioning methods used in this study. The RTK-DRTK2 method showed maximum errors of 0.067 and 0.054 m on the X-axis and Y-axis, respectively, while the RTK-DRTK2 + GCP method presented similar errors, with maximum values of 0.068 and 0.053 m on the X-axis and Y-axis. The RTK-CORS method presented the highest error on the X-axis with a maximum error of 0.071 m. However, the Y-axis error in the RTK-CORS method was similar to the one observed in the RTK-CORS+PPK method with a maximum error of 0.024 m.

Figures 7 and 8 show that all real-time position methods presented a slight variation in planimetry, with errors ranging from −0.071 m to 0.030 m for the X-axis and −0.025 to 0.055 m for the Y-axis. These planimetric errors were an order of magnitude less than the errors observed for altimetry. According to these results, a high planimetric accuracy was achieved in this study.

Figure 7

Errors in the X axis for each method evaluated.

Figure 8

Errors in the Y axis for each method evaluated.

The RMSE was calculated using equations (1)–(3). The RMSE _X,Y corroborates that the RTK-CORS+PPK method obtained the lowest planimetric error (RMSE _X,Y = 0.0164 m) (Table 1). In addition, it was shown that the RTK-CORS + PPK, RTK-D RTK2, and RTK-DRTK2 GCP methods presented very similar errors with a mean RMSE _X,Y value close to 0.05 m. Table 1 also shows that the RTK-DRTK2 + GCP method presented the lowest RMSEz value with 0.0201 m. However, similar RMSEz values of 0.0209 and 0.033 m were obtained for the RTK-DRTK2 and RTK-CORS + PPK methods, respectively. Based on the RMSEz values obtained, a high altimetric accuracy was obtained for the photogrammetric products.

The overall error value obtained (RMSE _X,Y,Z ) suggests that the best method to obtain photogrammetric products from orthophotos and DEMs using UAV is the RTK-CORS + PPK method. This method obtained an RMSE _X,Y,Z less than 4 cm. The method with the largest RMSE _X,Y,Z was RTK-CORS with 0.336 m. This high overall error was mostly influenced by the altimetric error since a low accuracy was obtained (RMSE _Z = 0.201 m). However, the RTK-CORS method presented an RMSEx,y comparable with the other real-time positioning methods used in this study (RMSE _X,Y = 0.0529 m).

To demonstrate if the accuracy observed is different for the different real-time positioning methods, a statistical analysis was carried out using an ANOVA (Table 2). This statistical analysis was carried out using the errors (difference between the estimated and the observed values) at each of the 26 CPs. This table shows the p-values obtained by using ANOVA, where a comparison of the four different methods was carried out using the X, Y, and Z axes errors as response variables.

For the Y axis, the ANOVA showed a p-value less than 0.05 indicating that there is a significant difference between the different methods tested. Hence, a multiple-range test was carried out to recognize the method with the lowest error (the most accurate method). Using the LSD method, this study demonstrated the existence of two homogeneous groups (Figure 9). This statistical analysis validated that the RTK-CORS and RTK-CORS + PPK methods showed the lowest error for the Y-axis. The mean error observed for these last two methods was close to zero. The ANOVA for the X-axis also demonstrated a significant difference between the different methods used (Table 2). Based on the LSD multiple range test, the RTK-CORS + PPK method showed higher accuracy in the X-axis and the error values obtained with this method are closer to zero. According to this statistical analysis, higher mean errors were observed for the other three real-time methods used.

Figure 9

Confidence interval plot for the errors obtained in the photogrammetric products when using four different real-time positioning methods.

Regarding altimetry (Z axis), the ANOVA showed that there is a significant difference between the different methods used (Table 2). Figure 7c shows 2 homogeneous groups: one homogeneous group comprised three methods, RTK-CORS + PPK, RTK-DRTK2, and RTK-DRTK2 + GCP, which are statistically equal (p-value > 0.05). The mean altimetric error obtained using these three methods was close to zero. According to these results, a high altimetric accuracy was obtained when using these three methods. The RTK CORS method was statistically different from the other three methods and showed a mean altimetric error difference of 0.15 m.

4 Discussion

Different techniques and methodologies are emerging to provide highly accurate photogrammetric products. The accuracy of these photogrammetric products using UAVs depends directly on a set of parameters, which include the geometric resolution of the sensor system, the longitudinal and transverse overlaps of the images acquired, the angle of the images, the UAV speed flight, the radiometric resolution of the images, among other parameters [20].

Accuracy analysis of photogrammetric products obtained using UAVs is generally performed using GCPs [25,56]. However, using GCPs has drawbacks, such as the time-consuming process of GNSS measurement and relatively higher costs. To overcome these challenges, certain techniques are used. One such technique is direct georeferencing on UAV, which is an aerial triangulation method that eliminates the need for GCP. By employing direct georeferencing techniques, field surveys can be reduced, resulting in the production of topographic maps with high accuracy [23]. This study provides a detailed comparison of four direct georeferencing methods used for digital photogrammetry: RTK-CORS, RTK-CORS + PPK, RTK-DRTK2, and RTK-DRTK2 + GCP. Based on the statistical analysis, the RTK-CORS + PPK method showed higher accuracy in planimetry, where the differences between the estimated and measured values were close to zero. When the RTK-CORS + PPK method was used, an RMSExy value of 0.0164 m was obtained. The planimetric accuracy using the RTK-CORS + PPK method suggests that the quality of photogrammetric products obtained can be comparable to the accuracy of LiDAR products [57]. According to Famiglietti et al. [41], the error range of RTK drones can be accurately measured up to 4.0 cm when used in conjunction with GCP. In this study, the enhanced accuracy of the RTK-CORS + PPK method was obtained, which measured up to 1.64 cm with very satisfactory results. These results can be attributed to the combination of RTK and PPK techniques. When RTK and PPK are used together, both real-time corrections and post-processing refinement produce a more thorough error correction and optimization of the data, resulting in improved accuracy levels.

Regarding the altimetric accuracy, no statistical differences were found between the RTK-CORS + PPK, RTK-DRTK2, and RTK-DRTK2 + GCP methods (p-value > 0.05). In the literature, the altimetric accuracy is reported as a function of GSD. Some studies based on traditional photogrammetry methodologies using GCP have reported an accuracy between 1 and 3 GSD, while planar topography projects range from 1 to 4.5 GSD [58,59,60]. For complex topography, RMSE _Z between 1.5 and 5 GSD are reported [39,61]. In the present study, an RMSE _Z between 1 and 1.6 GSD was obtained, except for the RTK-CORS method which presented an RMSE_Z close to 9 GSD. According to these results, the altimetric accuracy met the horizontal accuracy geometry at a scale level of 1:5,000 class and can be considered as high-precision geospatial data [23].

The maximum elevation difference of the photogrammetric products observed was 0.377 m when using the RTK-CORS method. This error can be considered as low vertical accuracy and could be related to some disadvantages or limitations observed with this technology. Since CORS transmits its real-time correction data via a cellular network, weak signal coverage could have compromised the availability and reliability of real-time corrections due to latency or delay in receiving the correction positioning data, reducing the accuracy of direct georeferencing. Despite this elevation difference, Elkhrachy [36] reported accuracies greater than 1 m for photogrammetric products that are not specific for topography or do not use GCP for ortho-rectification.

In this study, the influence of surface morphology on the planimetric and altimetric accuracy of RTK methods was evidenced. Greater elevation differences in altimetry were identified at CPs where slopes, ridges, valleys, bumps, and irregularities were present. Based on the results obtained in this study, surface irregularities introduced a change in photo scale and perspective distortions in the captured images. Therefore, the photo scale varied across the image in surfaces that showed significant relief or irregularities due to the changing distance between the camera and different parts of the surface. This variation in the photo scale affected the accurate measurement of distances and heights, leading to errors and inaccuracies in the resulting photogrammetric products [28,62].

Finally, several studies in the literature have proven that the use of UAVs with a large number of GCPs produces photogrammetric products with high accuracies, where RMSE _X,Y,Z of 0.06 m can be achieved [36]. According to Agüera-Vega et al. [61], when more GCPs are available, more triangulation can be performed between GCPs and image pixels. The direct georeferencing methods used in our study did not use GCPs for the development of the photogrammetric products, except for the RTK-DRTK2 + GCP method which used six GCPs. Despite this situation, a high planimetric and altimetric accuracy was obtained, similar to the accuracy of the photogrammetric products obtained using UAVs with a large number of GCPs or the one obtained in topographic surveys. Therefore, direct georeferencing methods demonstrated their feasibility of use in digital aerial photogrammetry with the advantages of low cost, time conservation, and minimum fieldwork [63,64]. Thereby, the RTK-CORS + PPK method can be used with full security, replacing the traditional methodologies, as long as there is a CORS antenna correction and internet signal. However, in remote locations where there is no internet, the RTK-DRTK2 and RTK-DRTK2 + GCP methods are suggested.

5 Conclusion

This study assesses the effect of traditional and current measurement technologies and methods, such as RTK, PPK, CORS, and RTK + GCP on the altimetric and planimetric accuracy of orthophotos and DEMs. According to the results obtained, the four methods showed acceptable accuracies in the planimetry, with a maximum value of RMSE _X,Y of 0.0529 m equivalent to almost 2.5 GSD. The RTK-CORS + PPK method was the most accurate in planimetry with an RMSE _X,Y of 0.0164 m (equal to 0.74 GSD).

In altimetry, three real-time positioning methods (RTK-CORS + PPK, RTK-DRTK2, RTK-DRTK2 + GCP) showed highly accurate photogrammetric products, with RMSE_Z values ranging from 0.0201 to 0.0334 m. Likewise, the results showed that the most accurate method was the RTK-CORS + PPK, which presented an RMSE _X,Y,Z of 0.0372 m for the three coordinate axes, while the RTK-CORS method was the least accurate.

This study found that three RTK methods (CORS-RTK + PPK, RTK-D 2RTK, and RTK-D 2RTK + GCP) effectively acquired topographic data. The planimetric accuracy of these methods achieved less than one GSD, while the altimetric accuracy was better than 1.5 times the value of the GSD. The accuracies obtained with these methods are comparable with topographic surveys that are measured in a traditional way using total stations or GNSS antennas. The photogrammetric products presented a high accuracy in DEM and orthophotography, with the advantage of a higher level of automation of these processes.

The present study demonstrated that various photogrammetric works can be performed with the RTK-CORS + PPK method without using GCP since this method produced acceptable results with RMSE of approximately 1–2 GSD in planimetry and 1.5–2.5 GSD in altimetry. This statement does not imply the elimination of CPs from photogrammetric flights, as these points are considered essential to validate the results obtained.