In South Africa, road maintenance and construction are the responsibility of the South African National Roads Agency Limited (SANRAL), which only accepts tenders for topographical road surveys carried out by conventional methods, in accordance with the Technical Methods for Highways (TMH 11) guidelines. The aim of this article is to investigate the height accuracies achievable under various conditions for GNSS observations and whether these can be used for topographical road surveys.
The advances of global navigation satellite systems (GNSS) in modern day surveys have become more precise and reliable in establishing three-dimensional (3D) co-ordinates in real time such that centimetre-level accuracy is achievable. The determination of heights using GNSS techniques is known to be less accurate than the determination of planimetric (y, x) co-ordinates.
Fig. 1: Relationship between the physical surface, geoid and ellipsoid. (priabroy.files.wordpress.com/2010/01/geoid-ellipsoidal-orthometric_height.jpg)
In South Africa, GPS is generally used for surveying purposes. Advances in satellite receivers have given rise to the development of receivers that have the function of observing a combination of GPS and GLONASS satellites, which result in an increased number of satellites to fix a 3D point. There are various factors which have an impact on the accuracy of GNSS height kinematic observations.
This article focuses on the use of differential carrier phase kinematic GPS and GPS+GLONASS observables in the context of general surveys where single base real time kinematic (RTK) GNSS will be used. It involves an investigation on the effect of observation interval (epoch) on achievable height accuracies using RTK GPS+GLONASS observations and the effect of achievable height accuracies using GPS and GPS+GLONASS observations at various observation intervals (epoch) in determining point heights. The effect of the geoid was not considered in this article.
Height measurements using GNSS
In 2008, the use of VRS GPS for road surveys was investigated by Robert Owen. In his research, he explores the creation of digital terrain models (DTM) by both VRS GPS and total station and makes a comparison between the two methods. Calibrated points were then placed using the VRS GPS survey method. The impact of these calibrated points on the established DTM was then assessed. A comparison between GPS and total station height accuracy was also analysed over a test field of 88 points. This was achieved by obtaining height observations of the 88 points by precise levelling, VRS GPS and total station. The levelled heights were taken as reference heights, and observations from the total station and VRS GPS were compared to the levelled heights. He concluded that the observations taken by GPS and total station were of the same magnitude [1].
Fig. 2: A flowchart illustrating the procedures carried out in the completion of this
research project.
In South Africa, the South African National Road Agency (SANRAL) is responsible for the maintenance and construction of roads. A practicing surveyor needs to tender for a topographical road survey on behalf of SANRAL, which is the body that allocates and approves the survey of South Africa’s roads. On the approval of a tender, SANRAL follows the guidelines of the TMH 11 documents [2].
The surface of the Earth is represented by the geoid, which by definition is referred to as “that equipotential surface of the Earth’s actual gravity field which on average coincides with mean sea level” [3]. The gravity potential along an equipotential surface is constant. The geoid is a mathematical model which is used as a reference surface for heights.
As illustrated in Fig. 1, we can see that the geoid is expressed as being between the physical surface (terrain) and the ellipsoid. The geoid and mean sea level depart from each other by less than or equal to 2 m, due to the effect of forces such as wind, pressure and ocean currents. The physical surface and the geoid are separated by no more than 8 km, whereas the ellipsoid and the geoid are separated by as much as 120 m. In general, height above the geoid, also known as the orthometric height, is used for surveying applications, but when using GNSS, heights above the ellipsoid are achieved. Thus, the reference surface for vertical heights when using GNSS techniques is given above the ellipsoid [3].
Fig. 3: Pictorial view of the structure of points within the test bed.
Methodology
A 1 km stretch of road was selected as the test site upon which all fieldwork was to be conducted. Permanent and clearly defined points along the road were precisely levelled between town survey marks (TSMs) and this served as the standard to compare the GNSS observations in order to make a valid comparison for accuracy. Fig. 2 defines the procedure followed in carrying out this article.
The test site selected needed to meet certain criteria in order to make valid comparisons. The criteria used to select the test site are the following:
Fig. 4: Observing points along the test bed using RTK GNSS.
Fieldwork involved the setting up of a single dense test site of 500 well-established and distributed (height) reference points along a 1 km stretch of road. The height of points in the test site will then be determined using both precise leveling and RTK GNSS observations. These observations will then be compared to each to make the necessary accuracy conclusions of RTK GNSS. The RTK GNSS observations will then undergo post-processing to model other variables as discussed. Fig. 3 illustrates the setup of the test bed.
Results and analysis
RTK GNSS observations
Once an orthometric height had been established for each point in the test bed, RTK (GPS+GLONASS) observations were observed and recorded using a RTK single base station method (position and height fixed to a known point). The elevation cut-off angle was set to zero degrees and GPS+GLONASS satellites were observed from both the base station and rover. These observations included all points in the test bed and at benchmarks. Three individual sessions, of varying observation interval (epoch in seconds), were observed. This included two sessions of 4 second epochs and a single session of 10 second epochs. The base station setup was established on the same known point for all three sessions and each point in the test bed and all benchmarks were observed to obtain a height observation for each point. During observations in the field, the geometric dilution of precision (GDOP) was kept to a minimum to ensure accurate observations were taken. Observations at both the base station and rover were recorded and stored during all fieldwork to allow for the processing of post processed kinematic (PPK) observations in the office.
| Session 1 4 Epochs (1) |
Session 2 4 Epochs (2) |
Session 3 10 Epochs |
|
| Total number of observations | 519 points (10 benchmarks) |
519 points (10 benchmarks) |
519 points (10 benchmarks) |
| Minimum GNSS satellites observed at once | 11 GNSS (6 GPS and 5 GLONASS) | 11 GNSS (6 GPS and 5 GLONASS) | 11 GNSS (7 GPS and 4 GLONASS) |
| Maximum number of GNSS satellites observed over entire session | 19 GNSS (14 GPS and 5 GLONASS) | 20 GNSS (14 GPS and 6 GLONASS) | 28 GNSS (19 GPS and 9 GLONASS) |
RTK (GPS+GLONASS) GNSS height observations were compared to precisely levelled points, which served as a standard for evaluating the achievable accuracy and precision of RTK GNSS. The 10 epoch session was then used in post-processing mode (PPK) to further analyse the achievable height accuracies of both GPS and GPS+GLONASS observations at five levels of observation interval (1, 2, 3, 5 and 10 epochs). Fig. 4 illustrates occupation of a point in the test bed.
The observations of three RTK (GPS+GLONASS), five PPK (GPS+GLONASS) and five PPK GPS were then analysed.
RTK (GPS+GLONASS) observations
Three RTK GPS+GLONASS observation sessions were observed in the field, which served the basis for analysis. Table 1 illustrates the number of points observed per session, minimum number of GNSS satellites observed at one given time per session and the maximum number of satellites observed overall within a session.
Fig. 5: A graph illustrating RMS and mean statistical measures for each RTK observation interval using GPS+GLONASS.
Each RTK (GPS+GLONASS) observation session was observed independently from each other as discussed previously. Both the 4 epoch (1) and 4 epoch (2) datasets present similar distribution patterns with an average height difference of -0,002 m and a RMS of 0,009 m as illustrated in Fig. 5. This would illustrate that on two different occasions, under different conditions, similar statistical results were achievable. The 10 epoch distribution has an average height difference of -0,001 m and a RMS value of 0,010 m as illustrated in Fig. 5.
This would illustrate that observing over a longer observation interval decreased the average height difference by a value of 0,001 m, but not the RMS value. Thus, increasing the observation interval increases the probability of achieving better results but does not increase the variation within the sample of data observed in the field.
Both 4 epoch samples illustrated the best percentage of observations falling within 1,0 cm accuracy with a percentage value of 84,01% and 99,23% of observations falling within a threshold of 2,5 cm. The 10 epoch sample had a percentage value of 81,31% within 1,0 cm accuracy and 98,84% within 2,5 cm. This illustrates that the probability of obtaining accuracy within 2,5 cm is achieved above 90,0% of the time using RTK (GPS+GLONASS) with various observation intervals. This is illustrated in Fig. 6.
GPS vs GPS+GLONASS observations
The following datasets were post processed using the 10 epoch RTK (GPS+GLONASS) sample:
Fig. 6: Threshold percentage levels for RTK (GPS+GLONASS) observations.
These GNSS observations were then compared to the precisely levelled point heights and differences between them calculated and analysed. A statistical comparison between the achievable accuracies of the above datasets was analysed in order to illustrate the effect of observation interval and GNSS type on fixing 3D co-ordinates (only the height component will be investigated).
A total of five observation intervals were assessed for GPS and GPS+GLONASS. The 10 epoch observation interval for GPS and GPS+GLONASS illustrates the greatest accuracy among the PPK results.
Fig. 7 illustrates that as the observation interval (epoch) increases so does the accuracy of both GPS and GPS+GLONASS height observations. For GPS only, the average height difference ranges between -0,003 m to -0,004 m, and the RMS ranges between 0,011 m to 0,014 m for the observation intervals investigated. For GPS+GLONASS, the average height difference ranges between -0,002 m to -0,003 m and the RMS ranges between 0,009 m to 0,011 m for the observation intervals investigated. The height accuracies achievable by GPS are similar to the height accuracies achieved by GPS+GLONASS, but the GPS+GLONASS height observations illustrate greater accuracy. The 10 epoch observation interval for GPS and GPS+GLONASS observations illustrate the greatest accuracy as expected. An RMS between 0,011 m and 0,012 m is achievable with GPS observations at the 5 and 10 epoch intervals, whereas a RMS of 0,009 to 0,010 m is achievable with GPS+GLONASS at the 3, 5 and 10 epoch intervals.
Fig. 7: A graph illustrating RMS and mean statistical measures for each PPK observation interval using GPS and GPS+GLONASS.
Fig. 8 illustrates the threshold levels for each GPS observation interval investigated. It can be seen that the 1 epoch represents the less accurate results, whereas the 10 epoch represents the greatest accuracy at each threshold level. For each epoch interval, 76% to 80% of the height observations are within an accuracy of 1 cm and 94% to 97% are within an accuracy of 2,5 cm. 97% of the observations of the 5 and 10 epoch intervals illustrate accuracy within 2,5 cm.
Fig. 9 illustrates the threshold levels for each GPS+GLONASS observation interval investigated. It can be seen that 1 epoch represents the less accurate results whereas the 10 epoch represents the greatest accuracy at each threshold level, except at the 1 epoch observation interval. A maximum of 83% of height observations are within the 1,0 cm threshold level, where the 10 epoch interval is the least accurate. For each epoch interval, 97% – 99% of the height observations are within an accuracy of 2,5 cm. 99% of the observations of the 3, 5, and 10 epoch intervals illustrate accuracy within 2,5 cm. 90% of the observations for each observation interval observed by GPS and GPS+GLONASS are within an accuracy of 2,5 cm, which is in accordance with the THM 11 guidelines.
Fig. 8: Threshold percentage levels for RTK (GPS-only) observations.
Conclusion
The accuracy of GPS and GPS+GLONASS height measurements are illustrated to be similar to heights established by precise levelling when using single base RTK GNSS. The RMS value for both 4 epoch sessions and the 10 epoch session are 9 mm and 10 mm respectively, and each epoch session illustrates that more than 90% of its observations are within 2,5 cm accuracy.
PPK GPS and PPK GPS+GLONASS observation sessions illustrate a maximum RMS of 14 mm with more than 90% of its observations within 2,5 cm accuracy among all observation sessions.
The comparison of RTK GNSS with levelling and the acquired RMS (between 0,009 m and 0,014 m) values provides strong evidence that GPS and GPS+GLONASS observations over short distances can achieve similar accuracies to conventional methods.
The main output from this article is that GPS and GPS+GLONASS can be used for road surveys, but this is highly dependent on the location of the road to be surveyed and its surroundings.
Fig. 9: A graph illustrating the percentage of observations which fall within a certain threshold level of each PPK (GPS+GLONASS) observation interval.
Recommendations
Acknowledgement
This paper includes research that was carried out in fulfillment of Muhammed Deal’s undergraduate studies at the University of Cape Town. The paper was presented at AfricaGEO 2014 and is republished here with permission.
References
[1] R Owen: Investigation into the use of VRS GPS for Road Surveys (Thesis), University of Cape Town, 2008.
[2] A Desai: Investigation into the use of Global Navigation Satellite Systems for topographical road surveys [Internal Report], Department of Rural Development and Land Reform. NGI: National Geo- Spatial Information, 2010.
[3] C Merry: “Geodesy, Lecture Notes”. University of Cape Town, Division of Geomatics, 2010, June.
[4] A El-Rabbany: Introduction to GPS – The Global Positioning System (Second Edition), The GNSS Technology and Application Series, E Kaplan, C Hegarty (Eds), Artech House Publishers, 2006.
Contact Muhammed Shaakir Deal, Department of Rural Development and Land Reform, Tel 021 658-4346, mdeal@ruraldevelopment.gov.za
