TS 5 – GNSS and Indoor Navigation 475 Rapid Establishing of Horizontal and Vertical Reference Frame using GNSS in Case of Large Engineering Projects Zoran Nedeljković 1 , Momir Mitrović 1 , Stevan Milić 1 1 University of Belgrade, Department of Geodesy and Geoinformatics, Bulevar kralja Aleksandra 73, Belgrade, Serbia, [email protected], [email protected], [email protected]Abstract. Defining reference system of an engineering project and its implementation can be done in several variants. There are a few main aspects that cause the type of implementation: territory size, accuracy, technology, time and money. This paper describes the variants that are analyzed and applied in the case study of the railroad reconstruction project, between Novi Sad and Hungarian border. This is the line type project with overall length of about 120 kilometers. Several important issues should be pointed out here: to build the frame with a little money, in a very short time, with centimeter level of accuracy, and finally to respect theoretical demands of such a big territory. Hence, it provides an opportunity to choose a timesaving variant, and frame implementation with GNSS technology seems to be very optimal. The works at the territory of such a size should take into account gravity aspect, for vertical frame. GNSS technology alone cannot solve this problem. Therefore, the reliance on the appropriate existing network with orthometric heights, allows indirectly the production of a height model. This paper analyzes main advantages and describes choice of optimal implementation type. All accomplished phases will be displayed in the paper along with the presentation of the achieved results. Keywords: coordinate system, GNSS, local geoid, orthometric height, photogrammetry, surface modelling. 1. Introduction to spatial coordinate system concept The term and idea of space is nearly connected with dimensionality. We can say that the concept of dimensionality depends on specific research areas. In geospatial and engineering applications, space is defined usually with three dimensions, based on the Euclidean paradigm of rectangular coordinate system [French & Ebison 1986]. The coordinate system can be defined, according to its purpose, at the micro level, locally, or universal level, globally. Geospatial studies are usually focused on the phenomena and processes that threaten the Earth as a global object being a general geographic area. On the other hand, the construction and engineering projects usually relates to a small local area. Satellite technology
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Rapid Establishing of Horizontal and Vertical Reference Frame using GNSS in Case of Large Engineering Projects Zoran Nedeljković1, Momir Mitrović1, Stevan Milić1
Abstract. Defining reference system of an engineering project and its implementation can be done in several variants. There are a few main aspects that cause the type of implementation: territory size, accuracy, technology, time and money. This paper describes the variants that are analyzed and applied in the case study of the railroad reconstruction project, between Novi Sad and Hungarian border. This is the line type project with overall length of about 120 kilometers. Several important issues should be pointed out here: to build the frame with a little money, in a very short time, with centimeter level of accuracy, and finally to respect theoretical demands of such a big territory. Hence, it provides an opportunity to choose a timesaving variant, and frame implementation with GNSS technology seems to be very optimal. The works at the territory of such a size should take into account gravity aspect, for vertical frame. GNSS technology alone cannot solve this problem. Therefore, the reliance on the appropriate existing network with orthometric heights, allows indirectly the production of a height model. This paper analyzes main advantages and describes choice of optimal implementation type. All accomplished phases will be displayed in the paper along with the presentation of the achieved results.
1. Introduction to spatial coordinate system concept
The term and idea of space is nearly connected with dimensionality. We can say that the concept of dimensionality depends on specific research areas. In geospatial and engineering applications, space is defined usually with three dimensions, based on the Euclidean paradigm of rectangular coordinate system [French & Ebison 1986]. The coordinate system can be defined, according to its purpose, at the micro level, locally, or universal level, globally. Geospatial studies are usually focused on the phenomena and processes that threaten the Earth as a global object being a general geographic area. On the other hand, the construction and engineering projects usually relates to a small local area. Satellite technology
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provides the use of globally defined and established coordinate system within the local scope in terms of its operation characteristics. There are two key components emphasized that characterize the coordinate system as an entity: the definition of the coordinate system and its realization or materialization.
The definition of the coordinate system is based on the abstraction of an observed object and recognition of its form and behavior in space and time [Kovalevsky & Mueller 1981]. In the Universe, where the constant movement and general positional relativity are recognized, the role of the coordinate system is to provide a temporary illusion of absolute spatial positions that is limited in its domain [Nedeljković & Sekulić 2016]. According to such abstract idea, the definition of a coordinate system should ensure its long life, or long enough to serve the main purpose. In defining the system, the needs of all current and future tasks that would eventually be covered must also be taken into account. The coordinate system is usually defined as a rigid structure that does not change over time (relative to the target object), especially not geometrically. A simple way to clearly determine position under, above and on the Earth's surface is to use a model of three-dimensional Cartesian coordinate system. The approximation of the Earth with flattened ellipsoid, gives the opportunity to represent previously defined coordinate system in an ellipsoidal, so called geographical model. The first model is Cartesian and it implies to the dimensionality of considered space. Second model is ellipsoidal and indicates to the shape of the Earth's figure and allows the choice between integrated or separated treatment of horizontal and vertical positions. Ellipsoidal model is used in the research of gravity field and, consequently, in defining the heights coordinate system. The aspect of cartographic applications is also still more easily implemented, using geographic coordinate system. Today is widely used term Mean Sea Level-MSL, which is viewed from the perspective of gravity, the closest to the geoid surface, consequently, to shape of the Earth. Normal line determines the height above ellipsoid and it has a mathematical importance for necessary calculations. The vertical line is used to determine the elevation, or in the case of geoid, the so-called orthometric height. Orthometric height has actually practical significance, because it reflects the natural phenomena of the site.
The implementation of the coordinate system is the process of its materialization. An entity that is physically visible and touchable is called the reference coordinate frame. The spatial disposition of network points, actually monuments of geodetic network, is designed to cover the observed object in the best way. When the global geodetic frame has to be built, the answer to the next important questions shall be given:
• To determine geometrical and geophysical relations between points of the network.
• Positioning and temporal changes of the network itself, within the scope of a globally adopted reference system.
In construction projects, only the first goal is often important. It is mostly not necessary to locate the observed object and its coordinate frame globally.
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The term “geodetic datum” usually includes both procedures: definition of the coordinate system and its implementation through a reference frame. In the glossary of the organization IERS, the term datum is described as follows [Petit & Luzum 2010]:
“Datum is a geodetic reference frame (plural datums). In surveying and geodesy, a datum is a set of reference points on the Earth's surface, and (often) an associated model of the shape of the Earth (reference ellipsoid) used to define a geographic coordinate system. Horizontal datums are used to describe the location of a point on the Earth's surface, in latitude and longitude or other appropriate coordinates. Vertical datums are used to describe site elevations or depths.”
Hence, the term “geodetic datum” refers to the integrated concept of coordinate system, which is recognized through geodetic network, its physical and visible marks and reference ellipsoid. Parameters of geodetic datum include three linear translations along coordinate axes X, Y and Z, three angular rotations around each of the axes and one scale parameter. Such datum parameters allow transformation between systems according to Helmert rules. Datum ellipsoid is determined by its semi-major axis a , and its coefficient of inverse flattening f/1. Thus, complete formulation of local geodetic datum, with its associated ellipsoid is specified by these nine values. From the historical point of view, in case of geographical model, it was important for the ellipsoid to be best suited to the local territory. Thus, there are many different ellipsoids used today, in different regions of the world. This is some kind of geodetic legacy and the existence of local ellipsoids and their enormous associated cartographic material, requires very extensive and complex tasks of transition. Not only their dimensions vary significantly, but also for obvious reason their spatial positions are also mutually different [Table 1.1]. This is especially important today when scientific research based on satellite technology and Geographic Information Systems (GIS) is rapidly developing. Table 1.1 Several examples of geocentric and local ellipsoids [NIMA 2000]
International 1924 6378388.000 297.000000000 -87.0 -96.0 -120.0
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The main problem and usual deadfall that can occur, is the irregular use of parameters from several geodetic datums, which are presents in different data sets. The disagreement between coordinate systems of spatial datasets can be recognized through two forms of appearance:
• Spatial datasets have the coordinate system defined on the same way, but implemented differently with different data.
• Datasets have two, or more differently defined and realized geodetic coordinate systems.
First case is often found in the exploitations of the geodetic survey systems from the past. It is reasonable to talk about geodetic networks that have never been implemented in the right way, or so-called “neglected” networks. Due to different reasons, important scientific facts have been often ignored and essential errors made throughout history, during the realization of the reference frame. The problem is even more significant because there is a huge amount of data systematically linked to the network [Blagojević 2009]. The second case is primarily of a logistic and organizational nature. Different coordinate systems can be transformed into a homogeneous unified datum in terms of their definition and realization. In order to solve this problem, it is necessary to adopt a target geodetic datum, and for these purposes, a global geocentric geodetic datum is often used.
2. Methods of establishing the reference frame
Construction projects are usually limited in areas, which depend on the project size, and are localized in the area of a few square kilometres. The road or railroad projects with line-type spatial structure and spreading in several hundred kilometres are an exception. Vertical component is a very important issue due to specific measuring technique and to the gravity effect. In a small project area, the coordinate system can be realized through simple geometrical aspect. The primary issue of reference frame, geometrical and geophysical relations between the points is always related to measurements. Network design and optimization, certainly should include accuracy, reliability and all appropriate metrological standards and rules. The secondary issue of the reference frame is the positioning of the network in globally adopted reference space and usually could be carried out with reliance to existing national networks.
In classical approach, horizontal frame can be determined by means of angle and distance measurements. It is appropriate to adjust such measurements in the network freely, without constraint. It is some kind of warranty that the mutual relations in the network are not artificially deformed. Horizontal coordinate system can be selected as a plane of cartographic projection, usually Gauss-Krüger. The reliance on the existing triangulation network and its datum parameters is of course a common practice. The selection of the local horizon plane as a coordinate system definition can be an alternative. There is one small, but essential benefit related to spatial distances. Namely, distances used in such defined coordinate system are closer to theirs measured values, compared with
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distances in cartographic projection plane. Bad aspect of local horizon mode is limitations of its area size. Both modes of defining the horizontal system can rely therefore on a global frame, or global enough, in the sense of countrywide network. That task can be done by transformation and is not always obligatory. The first reason for transformation is the usage of different pre-existing datasets and cartographic maps during construction process. The second reason is the relation with cadastral and urban planning procedures. The transformation should preserve geometrical relations between the points. Therefore is used transformation model where scale parameter is not evaluated.
Vertical reference frame is classically realized for construction projects based on the selected leveling method and adopted vertical origin. Vertical frame can be established with different optical instruments, such a spirit levelling instruments, or total stations with precise vertical angles measurements. In such case, the vertical origin can usually be defined arbitrarily and locally, according to the specific needs of construction project elements. On the other hand, the reliance on the existing vertical frame can always be an option. It is always the question of application features and further benefit of a frame. The same adjustment and transformation approach as taken in horizontal component is welcomed here. The measurements in network need to be adjusted freely, and data can be transformed without scale parameter evaluation.
Nowadays, the GNSS technology easily provides all three spatial coordinates in every specific point. Horizontal component has to be easily obtained. The conversion from Cartesian to ellipsoidal coordinate model, and cartographic projection to appropriate map plane can be performed unambiguously. Unfortunately, such determined height value does not reflect geophysical nature in the site. It is just a geometrically determined distance from surface of the datum ellipsoid to the point. As mentioned before, orthometric height is physically dependant on the gravity force. The usage of GNSS for vertical aspect can be possible only in modelling the height surface. Precise geoid model and orthometric heights are therefore the second part of 3D concept in GNSS technology. The measurements with GNSS can be performed statically or kinematically, depending from available infrastructure and accuracy demands. Static survey method is more accurate, but time-consuming variant. Kinematical method is faster, with smaller accuracy. However, the issue of accuracy in spatial applications is very relative category. Sometimes, the accuracy of 1-2 cm is unacceptable. It is however very useful for specific works. The scientific debate about difference between redundant measurements for network, and solely one measurement for just one field point, is old and might never ends. It is possible to overcome this misunderstanding today. The network of permanent GNSS stations is one of those steps forward. Such networks, can cover the whole national territory, and make a homogenous and accurate reference frame. The point position is obtained from at least three permanent stations using sophisticated checking and averaging procedures. Thus, it can be an option for more serious treatment of kinematical measurements in terms of reliability. Namely, several properly performed series of RTK epochs, in such infrastructure environment, can be treated as an adjusted value.
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The second part of the 3D reference frame puzzle is complex in itself. The geoid issue has their own complexity, and ways of its determination can be very different. One of simple approaches is to obtain discrete geoid undulation values, with appropriate density, in the area of interest. Satisfactory results can be obtained by relying on the existing precise levelling network. The density of national height network provides the possibility to make quite good surface model. Precise GNSS positions of specified marks with orthometric elevation need to be determined. More precisely, a provisional point close to the chosen elevation mark can be measured due to the functioning characteristics of GNSS. Orthometric height of such provisional point needs to be measured in spirit levelling manner. The model of such geoid undulation values, further is the matter of surface interpolation procedure. The surface can be modelled according to several surface approximation types [Cvijetinović 2005]:
• Polynomial regression (planar or quadratic) • Local polynomial (1st, 2nd or 3rd order) • Radial basis function, (Multiquadratic) • Kriging (linear Variogram model).
3. Case study: Reconstruction railroad project Novi Sad-Subotica
In this article is considered case study of railroad reconstruction project, located between city of Novi Sad and Hungarian border [Figure 3.1]. This is the line-type structure with overall length of about 120 kilometers. The reference frame is the basis for a draft project of railroad reconstruction. The data acquisition for the project is planned to be done mainly by means of photogrammetric method combined with additional terrestrial measurements. According to the scale of mapping of about 1:500 and 1:1000, the accuracy level of the measured points is expected to be within the range of 2-5 centimeters. The decision about the measurement methods used in the process of establishing the reference frame was made after all relevant criteria had been considered.
Main criterion aspects are: consuming time (it makes direct influence to the budget), project budget (include people and equipment engagement, with their daily costs), project size (indicates the gravity effect in the case of big size projects), optimal accuracy (it was considered accuracy in range from 0.1 cm to 3.0 cm) and dimensionality of the reference frame (in the meaning of a frame type: 1D, 2D and 3D). There are distinguished several implementation methods: classical triangulation with operational polygon, classical spirit levelling, GNSS static method, GNSS static method combined with height surface modelling, GNSS kinematical method (RTK series, obtained from permanent station network) and finally the same GNSS kinematical method combined with height surface modelling. The method with the highest score has been selected using a comparative table.
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Figure 3.1 Disposition of trigonometric points (triangles) and levelling marks (circles)
Score assignment for specific method, according to its criterion fulfillment, is given from 1 to 3 where bigger is better [Table 3.1].
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Table 3.1 Observation methods and suitability criterions (* denotes inappropriate method for specific project criterion)
The GNSS measurements based on permanent stations network and levelling
procedures was performed in 4 days. There were two one-man teams included, each having a car, GNSS rover receiver and level instrument [Figure 3.2].
During the campaign 20 trigonometric points and 41 precise levelling marks were observed [Figure 3.1]. The measurements on each mark were performed in 10 series, with 20 epochs per series and at least 10 paused epochs in between. It took practically almost 5 minutes per one possessed point. Such point's solutions are more reliable, with smaller correlation between epochs. The series were averaged, and each of them with the difference in coordinates of more than 1.5 cm from the mean value was discarded.
Horizontal component was solved using datum transformation from WGS84 to the National reference frame defined with Hermannskogel and Bessel ellipsoid parameters. Transformation parameters were evaluated with Helmert’s model of 6 unknown values: three translations and three rotations, using least square solution [Table 3.2]. Scale parameter was fixed. This approach gives larger residuals of frames disagreement, but relative distances are preserved from deviation, and complies with real values [Table 3.3].
Figure 3.2 Measurement procedure on the site
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The project area was treated as one integral space because of primary purposes of the construction project. Just to remind, the frame has the role to provide coordinate system implementation in the whole observed area. Hence, the division of the project area to smaller parts only for the purpose of satisfying the limit of residuals is not an option. Table 3.2 Datum transformation values
Evaluated 6 parameters (mo=0.390 m) Evaluated 7 parameters (mo=0.092 m) Translations: tx=-570.23310 m Translations: tx=-487.66777 m
ty=-175.92576 m ty=-146.38843 m tz=-464.95933 m tz=-375.70169 m
measurements, with ellipsoid heights determined by means of GNSS [Figure 3.2]. Such point collection, with discrete values of local geoid undulations, is used for height reference surface modelling [Figure 3.5]. Quality measure of surface approximation type is residual value of each point. The gravity field has homogenous effect locally, and local trends can be recognized quite clearly. The modeled surface should have therefore very smooth shape, without sharp jumps or falls [Figure 3.6].
Bearing this in mind, it should be decided which model type to adopt. Model approximation types, with their residuals are compared in [Table 3.4]. Table 3.3 Datum transformation residuals
Figure 3.5 Surface model contours produced with Surfer-8 software [URL 1]
Figure 3.6 Different surface models
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4. Conclusion
It is very clear that all basic requirements of the project have been met. The coordinate system with optimal accuracy has been accomplished in a short time, with a rather small budget. The mission was actually completed in five days, including additional computing and paper work procedures. The picture of accuracy is in fact a picture of the existing levelling frame. The analysis of surface model residuals can be done more in empirical way than by using the exact facts about the nature of the observed phenomena. There is no clear legitimacy for the selection of one or the other surfacing model. The model with the smallest residuals may be pretty fake and over-fitted. It cannot be so objective solution, having in mind poor condition of the existing levelling frame and GNSS accuracy limitations. The surface with large residuals that are the easiest to handle, is not representative for the project of such size. Thus, “the truth is somewhere in the middle”. The surface model with moderate residual values can be right solution. The layer of uncertainty of levelling network can be adopted as an objective zone of confidence, for the surface model. Final evaluation can be made in the inspection procedure when some check measurements need to be performed in the field. It is the final proof of the correct selection of a model. Furthermore, additional product of such height surface model is the elevation solution for small towns in the project zone. For example, the complete urban zone of the cities: Subotica, Bačka Toplola, Vrbas or even a large city of Novi Sad, can now have the possibilities for GNSS levelling. It is technically better solution because the model area is quite smaller, residuals are more realistic and without big strain.
References
Blagojević, D. (2009). Research of optimal model of horizontal transformation on the territory of the Republic of Serbia, Belgrade, Republic of Serbia-RGZ, Final Report.
Cvijetinović, Ž. (2005). Razvoj metodologije i tehnoloških postupaka za formiranje digitalnog modela terena za teritoriju države, doktorska disertacija, Građevinski Fakultet, Univerzitet u Beogradu, Beograd.
Kovalevsky, J.; Mueller, I. (1981). Comments on Conventional Terrestrial and Quasi-Inertial Reference Systems, Reference Coordinate Systems For Earth Dynamics, Warsaw, Proceedings of the 56th Colloquium Of The IAU Warsaw, Poland, September 8-12, 1981.
Nedeljković, Z.; Sekulić, A. (2016). Concept of spatial coordinate systems, their defining and implementation as a precondition in geospatial applications, Belgrade, Bulletin of the Serbian Geographical Society, Vol. 96, Issue 1.
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NIMA (2000). Technical Report, WGS84-It's Definition and Relationships with Local Geodetic Systems, U.S.A., Department of Defense.
Petit, G.; Luzum, B. (2010). IERS Conventions 2010 IERS-Technical Note No 36, Frankfurt am Main, Verlag des Bundesamts für Kartographie und Geodäsie.
URL 1: A Basic Understanding of Surfer Gridding Methods – Part 1, http://www.goldensoftware.com/newsletter/issue71-surfer-gridding-methods-part1, (17. 3. 2016).
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Brzo-uspostavljeni horizontalni i vertikalni referentni okviri pomoću GNSS-a za inženjerske projekte velikih razmjera Sažetak. Postoji više načina uspostave referentnoga koordinatnog sustava za potrebe inženjerskih projekata. Glavni čimbenici koji utječu na način uspostave su: veličina područja, točnost, tehnologija, vrijeme i novac. U radu su opisani i analizirani različiti načini uspostave te su primijenjeni na slučaju rekonstrukcije željeznice između Novog Sada i mađarske granice. Pruga predstavlja linijski objekt ukupne duljine oko 120 kilometara. Bitne činjenice o kojima treba voditi računa prilikom uspostave koordinatnog sustavu su: uspostaviti koordinatni sustav sa što manjim financijskim sredstvima, u što kraćem roku, sa centimetarskom točnošću te udovoljiti teorijskim zahtjevima tako velikog područja. Stoga se optimalnim pokazuje uspostava okvira pomoću GNSS tehnologije. Veliko područje radova zahtjeva da se za uspostavu vertikalnog okvira uzme u obzir i utjecaj gravitacije, što se ne može postići samo pomoću GNSS-a. Stoga oslanjanje na primjerenu postojeću mrežu s određenim ortometrijskim visinama indirektno omogućuje određivanje visinskog modela. U radu su analizirane glavne prednosti i opisan izbor optimalne uspostave referentnog okvira. U radu su prikazane sve dovršene faze i prezentirani postignuti rezultati.
