Introduction

In land surveying, there has always been discussion about the correct scope of use for geodetic observation instruments. In this regard, there is no doubt that GNSS and total stations are the most used, and therefore, the comparison between them arises immediately due to the great advances in both areas.

While it is true that GNSS and total stations are absolutely compatible with each other, the main problem lies in the representation of the resulting coordinates from certain observations. Also, the comparison addresses the precisions that both instruments could achieve, understanding that they are totally complementary techniques. This last point is key, since it is not possible to conceive the exclusive use of one technique given the productivity and precision requirements that frame a variety of projects.

 

Comparison Standard

In mathematical terms, a comparison can be expressed through a difference that aims to establish the proximity of a magnitude to a standard which must be close to the true value. Rather, it refers to the determination of an error.

To establish this error, the standard must be more precise than the value being compared. Therefore, for this experiment, it is considered that the determination of a total station will be more precise than that obtained by real-time GNSS positioning. However, it is extremely important to highlight that despite this consideration, the observations are complementary, and their combination is possible by taking the necessary precautions.

As mentioned previously, the standard is given by total station observations in the context of a terrestrial network which has high redundancy. A Trimble S5 total station with 1” angular precision and a 1 mm + 2 ppm distancer was used to observe, in cycles on both faces, a series of points distributed in a closed traverse of approximately 2000 m.

Fig 1. Trimble S Series

 

This geodetic network is calculated under SIRGAS, at an indeterminate epoch, on the UTM 19S projection and NMM heights, achieving an average precision of 95% of 18.0 mm in East, 17.6 mm in North, and 22.2 mm in elevation.

Fig 2. Geodetic network observed with Trimble S5 total station

 

GNSS Observations

On the same points of the previously indicated network, GNSS RTK observations were made with a Trimble R12i receiving differential corrections from the GEOCOM GNSS Network through the NTRIP service. All available constellations (GPS+GLO+GAL+BDS) and signals were used to perform the measurements, achieving baselines with lengths between 6.4 and 7.4 km.

The field survey considered the use of Trimble Access field software, which allows the development of automated workflows with a focus on highly efficient processes. Thus, during this experience, for the GNSS observations, baselines were established according to the following criteria available in Trimble Access:

  • Fast point: This is the simplest and most agile determination. It collects only a single observation (1 second).
  • Topographic point: This determination considers several observations over a defined time interval. For this example, 5-second topographic points are observed.
  • Observed control point: This is a 180-second topographic point. It is a predetermined Trimble method that guarantees the best RTK performance.

Fig 3. Measurement method in RTK under Trimble Access 2022.01

     

    For its part, RTK is a method primarily oriented towards performing topographic surveys. However, RTK observation based on the observed control point method provides room for addressing determinations that require more precision and reliability than a simple fast point.

     

    How different is a fast, topographic, and observed control point?

    On each point of the geodetic network, which already has precise coordinates established with a total station, different observations were made with Trimble R12i. In the same Trimble R12i setup, 3 baselines were measured using the methods described above.

    Fig 4. GNSS RTK determination

     

    Of the 25 points whose coordinates were calculated based on a total station, 17 were available and measured using the fast point and topographic point methods. Of the 17 occupied points, only 2 could not be measured using the observed control point method: one due to security issues and the other due to failure to achieve solution convergence.

    The following table shows a summary of the horizontal and vertical precisions obtained for each point:

     

    Horizontal Precision 95% (m)

    Vertical Precision 95% (m)

    Point

    Fast

    Topo

    Control

    Fast

    Topo

    Control

    0

    0.0119

    0.0119

    0.0083

    0.0260

    0.0258

    0.0213

    1

    0.0109

    0.0122

    0.0081

    0.0222

    0.0221

    0.0191

    2

    0.0150

    0.0149

    0.0112

    0.0319

    0.0317

    0.0297

    3

    0.0180

    0.0179

    n/a

    0.0319

    0.0312

    n/a

    4

    0.0183

    0.0182

    0.0166

    0.0449

    0.0451

    0.0416

    6

    0.0140

    0.0134

    0.0098

    0.0390

    0.0369

    0.0289

    8

    0.0137

    0.0135

    0.0101

    0.0352

    0.0347

    0.0312

    9

    0.3415

    0.3535

    n/a

    1.7283

    1.8138

    n/a

    10

    0.0237

    0.0222

    0.0154

    0.0483

    0.0461

    0.0352

    13

    0.0189

    0.0192

    0.0164

    0.0389

    0.0381

    0.0388

    15

    0.0177

    0.0180

    0.0141

    0.0363

    0.0368

    0.0338

    17

    0.0176

    0.0181

    0.0148

    0.0297

    0.0310

    0.0269

    18

    0.0405

    0.0340

    0.0241

    0.0686

    0.0690

    0.0413

    19

    0.0155

    0.0149

    0.0095

    0.0283

    0.0264

    0.0199

    20

    0.0174

    0.0220

    0.0081

    0.0337

    0.0440

    0.0179

    21

    0.0164

    0.0165

    0.0126

    0.0292

    0.0323

    0.0264

    22

    0.0116

    0.0116

    0.0081

    0.0232

    0.0233

    0.0192

    Table 1. Precisions at 95% for each determination with Trimble R12i

     

    After eliminating point 9, the following average precisions are obtained:

    Method
    Horizontal Precision (m)
    Vertical Precision (m)
    Fast point
    0.0176
    0.0355
    Topo point 5 s
    0.0174
    0.0359
    Observed control point
    0.0125
    0.0287

    Table 2. Summary of average precisions obtained in all observations

     

    Performing the comparison

    The observations made with Trimble R12i originated from the SNTI station, whose coordinates are adjusted to SIRGAS-Chile 2021. However, the geodetic network observed with the total station had an origin given by a SERVIU vertex with an unknown epoch. The latter presents one of the great current challenges, which is the harmonization of epochs and reference frames. In relation to the above, it was necessary to link the SNTI station to the SERVIU origin point to make a correct comparison. The results obtained show centimeter-level precision for real-time observations with determinations in limited time intervals, which favors field productivity.

    Fig 5. Origin of observed GNSS baselines

     

    Once this linkage is made, both sets of coordinates, GNSS and total station, have the same reference and can be compared.

    Finally, the difference between the calculated position of the total station and that obtained by each method applied in GNSS is calculated, achieving the root mean square error:

    Method

    East (m)

    North (m)

    Elevation (m)

    Observed control point

    0.0315

    0.0480

    0.1117

    Topo point 5 s

    0.0232

    0.0419

    0.1242

    Rapid point

    0.0203

    0.0409

    0.1126

    Table 3. Root mean square error of each solution

     

    Analysis

    The Trimble R12i's real-time processing engine was vital to the receiver's performance in this test. In addition, the IMU incorporated in Trimble R12i allowed for improved positioning through an observation of inclination and orientation that completes the mathematical positioning model.

    The rapid point and topo methods use the IMU to determine the inclination and orientation of the antenna, which means the pole can be set up non-vertically. On the other hand, the observed control point method eliminates the IMU operation, which indicates that the antenna must be installed very precisely over the point, focusing entirely on obtaining a high-precision satellite observation.

    Fig 6. GNSS observation using pole and bipod

     

    Thus, the positions obtained by rapid point and topo are corrected for the effect of the pole's inclination, while those determined by observed control point are not. This is important when conducting the analysis because the datasets describe different effects.

    Fig 7. Observed control point vs. rapid point: in the first case, the IMU is not being used, while in the second case, it is.

      

    If the rapid point and topo solutions are combined and compared with the observed control point determinations, the error in the pole setup can be seen. This allows us to conclude that the observed control point method requires a much more precise setup, preferably performed with a tripod and leveling base.

    Finally, the root mean square setup error is 14 mm in east, 20 mm in north, and 14 mm in elevation.

    Regarding the results obtained in the direct comparison of total station and GNSS, several factors must be considered:

    • Baseline length: baselines of around 7 km can be determined. Better results can be obtained by reducing the baseline length.
    • Satellite observation situation: the environment was genuinely complicated given the characteristics of an urban site. However, all solutions yielded very similar results, which speaks well of the real-time processing engine.
    • Lack of geoid modeling: a baseline determined with GNSS allows direct evaluation of the height difference between ellipsoidal heights. If conversion to a height difference of physical heights is desired, a much more detailed geoid modeling is necessary. In this example, EGM08 was used, but even so, the length of the observed baselines was too long to adequately evaluate the effect of the heights. The 11.6 cm difference can be significantly improved by reducing the baseline length or using a vertical correction surface.

    Regarding height, the most convenient way to compare is through the elevation difference. In this way, different sections are established for comparison, obtaining a root mean square error of 38.3 mm. The details are as follows:

    Elevation difference

    TS (m)

    GNSS (m)

    Difference (m)

    0-1

    -3.4310

    -3.4459

    0.0149

    1-2

    3.3097

    3.3224

    -0.0127

    2-4

    -6.0245

    -6.0176

    -0.0069

    4-6

    -0.2072

    -0.2222

    0.0150

    6-8

    -1.0184

    -0.9823

    -0.0361

    8-10

    -4.1935

    -4.2289

    0.0354

    10-13

    -1.7057

    -1.6735

    -0.0322

    13-15

    -2.6960

    -2.6948

    -0.0012

    15-17

    -1.5660

    -1.5368

    -0.0292

    17-18

    0.7956

    0.7173

    0.0783

    18-19

    -0.5810

    -0.5193

    -0.0617

    19-20

    3.9200

    3.9056

    0.0144

    20-21

    2.9791

    3.0208

    -0.0417

    21-22

    3.9390

    3.8691

    0.0699

    22-1

    3.0489

    3.0402

    0.0087

    Table 4. Comparison of elevation differences obtained by total station and GNSS

     

    Conclusions

    Definitely, total station and GNSS observations can be combined. This is a fact widely supported by academia through the relationship between the geocentric and topocentric systems given by the relationship of the geodetic and physical normal (or plumb line). However, the major problem in the industry is obtaining coordinates between one instrument and another. This presents an interesting challenge that must be addressed by geomensuration.

    Now, in technological terms, Trimble R12i, through ProPoint and TIP, provides an extremely precise solution that can perfectly be considered as a complement to total station observations, addressing the need for field productivity. In terms of GNSS observation, the presence of ProPoint and TIP provides a robust and reliable solution that can be integrated into total station determinations in various scenarios.