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New information and communication technologies have led to the emergence of new techniques in our daily lives. Indeed, in topography, a lightning development of new techniques and new devices has been noticed. This development has given rise to a multitude of choices of devices and various classes of precision. This implies that the decision-makers have to study the adequate equipment and the appropriate technique according to the topographic task to be realized. The objective is not to compare GNSS and topographic techniques, but to point out the contribution of the Global Navigation Satelite System (GNSS) techniques of topographic work. Thus, a theoretical study with a critical eye on the scientific principle of calculating the third topographic dimension followed by a leveling campaign, Real Time Kinematic (RTK) surveys will be used in order to be able to compare and interpret the result from these campaigns. The study of the difference resulting from the practical campaigns will allow us to identify the contribution of GNSS technology.

The execution of topographic work usually requires the prior existence of geodetic benchmarks to be used for referencing the data from the measurements. With the Spatial Positioning System, most reference points are now directly determined in 3D.

In order to meet this requirement, a durable network of points is needed to determine the planimetric and altimetric positions of objects (or points) on the earth’s surface. In Senegal, the 1953 General Levelling of West Africa (NGAO53) and the 2004 Reference Network of Senegal (RRS04) are the official height and planimetric reference systems. It should be noted that the determination of heights generally poses more problems for professionals in countries such as Senegal, where height benchmarks are not as accessible [

In this work, the contribution of Global Navigation Satellite System (GNSS) technology to the estimation of the third dimension is highlighted. Thus, leveling campaigns and GPS surveys were carried out in order to identify the contribution of GNSS technology in topography. Following the direct leveling operations, Real Time Kinematic (RTK) and fast static surveys were carried out with the integration of the EGM2008 geoid model for the determination of heights from the determined heights and interpolated undulations. A comparison of these two types of measurements was used to assess the accuracy of EGM2008 in the study area.

Direct leveling or geometric leveling is a topographic operation carried out with the aid of a level and a staff, which makes it possible to determine the difference in level (commonly known as geometric height difference) between two points from horizontal sights taken on a staff. The calculation of heights from this operation is based on the knowledge of the level differences and the initial height [

This operation is often used in topography to perform a height adjustment, which requires a vertical reference network.

Of course, the level difference between two points does not depend directly on the path followed, unlike measured differences in level ( [

The back and front readings vary with the path followed and the height of the station, whereas the difference in level along a chosen path depends on the back and front readings. Analysing the elevation potential, it becomes clear that it is not the elevation difference that is a constant but rather the potential difference ( [

On the other hand, considering this element as such, it would be interesting to apply Schwartz’s theorem on the total differential. The application of this formula on the level difference is given by equation number 1 below:

∂ 2 d n ∂ L a r ∂ L a v = ∂ ∂ L a r [ ∂ d n ∂ L a v ] = 1 ? (1)

Applying this formula actually gives a null value to the double differential: this shows that the gradient is not a state function. In a classical way, this difference in level remains a constant between two points. But in the case where one of the points would have undergone a movement then this difference in level becomes a variable function with the environment of measurement that we could estimate. Could a monitoring study within the framework of auscultation estimate in a particular way this temporal variation?

For a path between two points, there is a link between the backward and forward readings. There is a real such that:

l a r = l a v + ε (2)

ε is such that the height difference between these two points remains constant. Therefore, ε does not vary and remains constant.

Thus, the difference in level can be expressed as such:

d n = l a v + ε − l a v = ε = c s t e (3)

∂ ∂ d n ∂ L a r ∂ L a v = 0 (4)

The contradiction between (1) and (4) is an actual limit of direct leveling.

Satellite positioning systems have made a great contribution to the accurate determination of points on the earth’s surface. However, the determination of the altimeter component was one of the limitations of this system, as it could only measure the height relative to the associated ellipsoid. This did not correspond to the physical quantity (altitude) that users were interested in. It was not until the development of geoid models that could be integrated into GNSS receivers or calculation software to obtain heights from these measurements and the undulation provided by the model. Several models have been implemented such as EGM 96 and EGM08.

The functions used to determine the ripples are calculated according to harmonic models [

The ripples associated with the EGM08 model are calculated on each of the grid nodes with harmonic functions expandable to degrees n. ( [

N = T γ = G M γ ∑ n = 2 ∞ a e n r n + 1 ∑ m = 0 n P n , m ( sin φ ) ( C n , m ∗ cos m λ + S n , m ∗ sin m λ ) (5)

The objective of this paper is to highlight the contribution of GNSS in some conventional surveying work.

The approach adopted is to establish a base polygon by conventional surveying methods. The different points of the polygon were also observed by GNSS methods (RTK and fast static).

The second part consists of studying the altimetric coupling of GNSS and the conventional method. Knowing the order of magnitude of the differences, a study is conducted to reconcile the two methods.

The study area is located in Thies, more precisely in the HLM district of Mbour, just to the right of the road leading to Mbour at the level of the Lat. Dior stadium. The geographical coordinates of the study area vary in longitude between −16.945˚ and −16.950˚ and in latitude between 14.774˚ and 14.776˚.

The study area is illustrated in

GNSS observation in fast static mode is becoming increasingly easy ( [

Stations | ΔE (m) | ΔN (m) |
---|---|---|

K1 | 0 | −0.001 |

K2 | −0.002 | 0 |

K3 | 0 | −0.003 |

K4 | −0.002 | 0.008 |

Δφ (˚) | Δλ (˚) | |
---|---|---|

K1 | −0.01112 | −0.00280 |

K2 | −0.00147 | 0.06053 |

K3 | −0.03254 | 0.00424 |

K4 | 0.07668 | 0.04583 |

In this section, the graph shows that small (millimeter) deviations were obtained between the RTK and fast static solutions. These small differences in our case are mainly due to the short baselines obtained. These could quickly reach the centimeter (or even a few centimeters) if the baselines exceeded ten kilometers. This could make fast static positioning acceptable in contrast to RTK. It would therefore be better to proceed with the central pivot method, which would consist of creating and calculating a first station centred in the study area by static or fast static methods (depending on the baseline). This station would then serve as a pivot for the different observations in fast static mode or in RTK (if the baselines are weak) as in our case. This would guarantee a certain accuracy and speed.

For this phase, a framed polygon between points K3 and K2 was made. To do this, angle and distance measurements were made on each vertex of the polygon. The result is tabulated in

The advantage of this method is that it has the particularity of being the possible technique for making a canvas when the conditions for using GNSS are not met, a possibility for working indoors as well as outdoors. It usually requires a team of three people, including a chief surveyor, an operator, a survey assistant and possibly a driver.

The disadvantage of this method is that it requires a lot of time for execution and precision depending on the length of the sides of the polygonal. Also, it is

Stations | Target Point | Distances | Angles | Gisement |
---|---|---|---|---|

K3 | K2 | 174.015 | 273.8444 | 323.822283 |

ST1 | 397.666683 | |||

ST1 | K3 | 80.281 | 300.5506 | 197.666683 |

ST2 | 98.217283 | |||

ST2 | ST1 | 155.479 | 296.6812 | 298.217283 |

ST3 | 194.898483 | |||

ST3 | ST2 | 48.564 | 124.44167 | 394.898483 |

ST4 | 119.340153 | |||

ST4 | ST3 | 101.38 | 74.1056 | 319.340153 |

ST5 | 393.445753 | |||

ST5 | ST4 | 93.297 | 313.3 | 193.445753 |

ST6 | 106.745753 | |||

ST6 | ST5 | 85.682 | 229.6805 | 306.745753 |

ST7 | 136.426253 | |||

ST7 | ST6 | 118.682 | 188.3749 | 236.426253 |

ST8 | 124.801153 | |||

ST8 | ST7 | 77.998 | 107.2648 | 324.801153 |

K1 | 32.065953 | |||

K1 | ST8 | 228.169 | 392.5553 | 232.065953 |

K2 | 224.621253 |

only carried out during the day, a restriction due to the total station. It also requires the knowledge of two or more landmarks. Also, it has a low dependency on the measurement environment, some interoperability problems (Prism Constant), independence from external structures. It is generally more easily influenced by certain sources of error.

After the field phase, the raw data has to be compensated when the closure is below the tolerance. This processing can be done with topometric software, by hand calculation or in Excel. This processing can take several tens of minutes compared to the GNSS method.

The financial costs for the realization of this method are variable and depend on the number of staff and the execution time as well as on the expected accuracy.

Three points were surveyed by RTK method. The result of this survey is listed in

Angular closing (mgon) | −3.5825 |
---|---|

f a = G arrivedobs − G arrived | |

Planimetric closure (cm) | 7.18 |

f p = f X 2 + f Y 2 | |

Compensation | |

C i = − f a ∑ i = 1 n p i ∗ p i | |

Angular tolerance (mgon) | 18.35 |

12.96 + 36 ( n + 1 ) | |

Planimetric tolerance | 14.15 |

16 + 16 n + 160 ∑ i = 1 n L i 2 |

STATIONS | E (m) | N (m) |
---|---|---|

ST1 | 290,117.9530 | 1,634,401.8200 |

ST2 | 290,198.2000 | 1,634,404.0699 |

ST3 | 290,210.6420 | 1,634,249.0952 |

ST4 | 290,256.9780 | 1,634,234.5745 |

ST5 | 290,246.5590 | 1,634,335.4269 |

ST6 | 290,339.3300 | 1,634,325.5622 |

ST7 | 290,411.3600 | 1,634,279.1717 |

ST8 | 290,521.1450 | 1,634,234.0976 |

STATIONS | E (m) | N (m) |
---|---|---|

ST2 | 290,198.184 | 1,634,404.082 |

ST3 | 290,210.615 | 1,634,249.054 |

ST6 | 290,339.273 | 1,634,325.545 |

The comparison of coordinates between RTK and base polygon surveys is shown in

Comparing the coordinates obtained by the fast static method and by the RTK method, it is noted that the differences between these two methods are millimetric in our practical case. In the logic of noting these differences in accuracy, a comparison of the coordinates obtained by RTK method and by classical polygonation method has been made.

STATIONS | ∆E (m) | ∆N (m) |
---|---|---|

ST2 | −0.016 | 0.0121 |

ST3 | −0.027 | −0.0412 |

ST6 | −0.057 | −0.0172 |

In summary, the coordinates calculated and compensated by the polygonal method are close to the RTK coordinates by a few centimeters. Using the conventional method for this type of work requires a lot of set-up and tedious work. GPS saves time and reduces the cost of the work with less risk.

The polygonation method therefore requires more time and a team of more than three people. It gives a centimetric accuracy compared to the coordinates obtained by GNSS post-processing.

The method adopted for connecting the points of the polygon is direct leveling. This method has the following advantages: spontaneous reading of the difference in level, ease of implementation, speed of measurement and millimeter accuracy.

The disadvantages of this method are the limitation of the ranges due to the instrument used, the dependence on the measuring environment, a problem of visibility between two successive measuring points and numerous stations when the points are far apart.

This leveling operation will make it possible to find the altitude of the base points in the study area. It will allow comparison of the variations in undulations deduced by post-processing and by RTK.

A closed path is applied to point TH02. After completing this path, which contains point K1, another closed path is performed around K1 to find the altitude of the post-processed points.

From point K1, the heights of the other points are found. This path is given in

According to [

The tables summarise the deviations of the geographical coordinates of points K1, K2, K3 and K4 and the variation of the undulations. These variations have been calculated with reference to the coordinates and waviness of point K1.

Tolerance in mm | n ≤ 16 | n > 16 |
---|---|---|

ordinary | 4 ∗ 36 ∗ L + L 2 | 36 ∗ N + N 2 / 16 |

accuracy | 4 ∗ 9 ∗ L + L 2 | 9 ∗ N + N 2 / 16 |

High accuracy | 8 ∗ L | 2 ∗ N |

With n= N/L (in Km).

Points | DIST | LAR | LAV | ∆N | ALTI | C/∆N | ALT (comp) |
---|---|---|---|---|---|---|---|

TH02 | 1664 | 90.117 | 90.117 | ||||

1 | 80 | 1462 | 1701 | −0.037 | 90.08 | 0.00012731 | 90.080 |

2 | 100 | 1394 | 1396 | 0.066 | 90.146 | 0.00022709 | 90.146 |

3 | 110 | 1323 | 1300 | 0.094 | 90.24 | 0.00032343 | 90.240 |

4 | 130 | 1526 | 1525 | −0.202 | 90.038 | 0.00069503 | 90.039 |

5 | 110 | 1132 | 1186 | 0.34 | 90.378 | 0.00116985 | 90.379 |

6 | 120 | 818 | 872 | 0.26 | 90.638 | 0.00089459 | 90.639 |

K1 | 120 | 1182 | 1214 | −0.396 | 90.242 | 0.00136253 | 90.243 |

7 | 120 | 2123 | 2093 | −0.911 | 89.331 | 0.0031345 | 89.334 |

8 | 120 | 1605 | 1498 | 0.625 | 89.956 | 0.00215045 | 89.958 |

9 | 120 | 1704 | 1662 | −0.057 | 89.899 | 0.00019612 | 89.899 |

10 | 100 | 1692 | 1693 | 0.011 | 89.91 | 3.78E−05 | 89.910 |

11 | 100 | 1676 | 1693 | −0.001 | 89.909 | 3.4407E−06 | 89.909 |

12 | 100 | 1618 | 1617 | 0.059 | 89.968 | 0.000203 | 89.968 |

TH02 | 100 | 1480 | 0.138 | 90.106 | 0.00047482 | 90.117 |

Points | Distance | LAR (mm) | LAV (mm) | Dénivelée (m) | ALT (m) | Comp (m) | ALT (comp) |
---|---|---|---|---|---|---|---|

K1 | 2011 | 90.243 | 90.243 | ||||

1 | 110 | 1253 | 1252 | 0.759 | 91.002 | 0.001854 | 91.004 |

K2 | 160 | 1238 | 1207 | 0.046 | 91.048 | 0.000112 | 91.050 |

3 | 100 | 1370 | 1414 | −0.176 | 90.872 | 0.00043 | 90.874 |

4 | 130 | 569 | 585 | 0.785 | 91.657 | 0.001917 | 91.661 |

5 | 130 | 1748 | 1728 | −1.159 | 90.498 | 0.00283 | 90.505 |

K3 | 120 | 1595 | 1588 | 0.16 | 90.658 | 0.000391 | 90.666 |

6 | 100 | 1565 | 1560 | 0.035 | 90.693 | 0.0000855 | 90.701 |

7 | 100 | 1187 | 1157 | 0.408 | 91.101 | 0.000996 | 91.110 |

K4 | 130 | 2231 | 2293 | −1.106 | 89.995 | 0.002701 | 90.006 |

8 | 130 | 1140 | 1146 | 1.085 | 91.08 | 0.00265 | 91.094 |

9 | 100 | 1207 | 1240 | −0.1 | 90.98 | 0.000244 | 90.994 |
---|---|---|---|---|---|---|---|

10 | 100 | 1528 | 1536 | −0.329 | 90.651 | 0.000803 | 90.666 |

11 | 120 | 1411 | 1422 | 0.106 | 90.757 | 0.000259 | 90.772 |

12 | 130 | 1360 | 1381 | 0.03 | 90.787 | 0.0000733 | 90.802 |

13 | 130 | 1793 | 1779 | −0.419 | 90.368 | 0.001023 | 90.384 |

14 | 100 | 2190 | 2142 | −0.349 | 90.019 | 0.000852 | 90.036 |

15 | 160 | 1767 | 1747 | 0.443 | 90.462 | 0.001075 | 90.480 |

K1 | 110 | 2005 | −0.238 | 90.224 | 0.000703 | 90.243 |

Points | Altitudes |
---|---|

K1 | 90.243 |

K2 | 91.050 |

K3 | 90.666 |

K4 | 90.006 |

Points | h (RTK in m) | Altitude (GL in m) | N (m) |
---|---|---|---|

K1 | 120.757 | 90.243 | 30.514 |

K2 | 121.555 | 91.048 | 30.507 |

K3 | 121.163 | 90.658 | 30.505 |

K4 | 120.519 | 89.995 | 30.524 |

It is noted that when the deviation in longitude and latitude is of the order of a millimeter, then the ripple variation is below a meter.

It is also noted that, for three points, when the deviation of longitudes is constant and the deviation of latitudes varies, the variation of the ripples is metric. This result therefore shows that the ripple varies with latitude.

Moreover, for three points, the latitude differences between these three points are close and the longitude differences vary. So, the variations of the ripple depend on the variations of the longitude.

Moreover, the ripple is a variable that depends on the variations of longitude and latitude.

The mean square error (emq) is: σ = ±0.041 m. The value found verifies well the accuracy of EGM08 which is of the order of 5cm in Senegal [

It is summarised in

Points | Longitude (˚) | Latitude (˚) | ∆λ | ∆ϕ | N | ∆N |
---|---|---|---|---|---|---|

K1 | −16.94580364 | 14.774593 | 30.514 | |||

0.00078232 | 0.00191619 | −0.007 | ||||

K2 | −16.94658596 | 14.77267681 | 30.507 | |||

0.00402867 | 0.00070723 | −0.009 | ||||

K3 | −16.94983231 | 14.77388577 | 30.505 | |||

0.0042569 | 0.00202804 | −0.010 | ||||

K4 | −16.95006054 | 14.77662104 | 30.524 |

Points | Altitude (NG) | Altitude | Différence | Ondulation |
---|---|---|---|---|

K1 | 90.243 | 90.286 | −0.043 | 30.514 |

K2 | 91.048 | 91.084 | −0.036 | 30.507 |

K3 | 90.658 | 90.697 | −0.039 | 30.505 |

K4 | 89.995 | 90.04 | −0.045 | 30.524 |

This means that for studies (e.g., pre-project) or leveling works that have to be carried out with a tolerance of a few centimeters, an accurate global geoid model such as the EGM2008 could be used. However, the best solution is still to use a local geoid model, as is the case in many developed countries.

From these results, the contribution of GNSS in terms of altimeter linking is highlighted. However, it is important to keep in mind that despite the approximation of the results, geometric leveling remains the most accurate operation to altimetrically link a point.

This study has helped to understand and establish the limitations of GNSS and conventional surveying.

It also allowed answering several questions raised between GNSS and conventional topography.

The results of this study have shown the contribution of GNSS in terms of time saving and accuracy and under certain constraints.

It should be noted that these contributions currently concern all the classical domains except leveling when the environmental conditions allow the use of GNSS. But, nevertheless, it should just be known that with some treatments reported in our studies, GNSS can come close to direct leveling when associated with a global geoid model such as EGM2008. Leveling remains the field of topography where GNSS does not yet give very satisfactory results by simple use in countries such as Senegal where we note an absence of a precise local geoid model that could be derived from gravimetric, leveling and GNSS measurement campaigns.

We thank all those who have contributed to the production of this document.

We declare no conflict of interest for this document.

Ly, C.A.T., Diene, J.M.L., Diouf, D. and Ba, A. (2021) GNSS Technology’s Contribution to Topography: Evaluative Study of Gaps between Methods Topographies. Journal of Geographic Information System, 13, 340-352. https://doi.org/10.4236/jgis.2021.133019