TESTING THE REPEATABILITY OF RESULTS USING THE GNSS-RTK MEASUREMENT METHOD

Stefan Miljković 1 Jelena Gučević 2 Siniša Delčev 3 Vukan Ogrizović 4 Miroslav Kuburić 5 UDK: 528,06 DOI: 10.14415/konferencijaGFS2019.101 Abstract: The paper presents the concept of the AGROS network of permanent stations and describes the procedure for implementing the service for real-time kinematic positioning (AGROS-RTK). Experimental research was conducted with the aim of testing the reliability and accuracy of the AGROS network of permanent stations in the RTK mode. Testing was carried out on a polygon of stable geodetic points. Observations were performed once a year for a period of three years. The results analysis shows that there are differences among the epochs and that the possible causes need to be further examined.


INTRODUCTION
The network of permanent stations CORS (Continuously Operating Reference Stations is a set of properly distributed GNSS receivers, operating within a single system, continuously for 24 hours a day. The main task of the system is to enable precise positioning using one GNSS receiver. Reference stations are linked to the control centre that controls their work and distributes the necessary data. Networks are most often formed at the national or regional levels and represent the reference framework of the system present in the area [6]. The network of permanent GNSS stations, officially in use on the territory of the Republic of Serbia, is called the Active Geodetic Reference Network of Serbia (AGROS) and is owned by the Republic Geodetic Authority. It is comprised of 30 7. МЕЂУНАРОДНА КОНФЕРЕНЦИЈА Савремена достигнућа у грађевинарству 23-24. април 2019. Суботица, СРБИЈА operating GNSS receivers properly distributed on the territory of the country with an average distance of about 70 km [4]. The AGROS User Centre offers several services to its users, the most commonly used being corrections for real-time kinematic positioning (AGROS-RTK). Within the AGROS-RTK service, it is possible to carry out all geodetic measurements for the purpose of geodetic surveying, as well as for various engineering projects. The prescribed accuracy allowed by the AGROS system can be achieved only if the prescribed procedure is followed during measurement, and it is therefore of utmost importance to comply with all the measurement instructions. Regarding monitoring accuracy and reliability of the results obtained by using the AGROS-RTK service, there are no established parameters that can efficiently monitor the declared accuracy at any time and place.

RESEARCH OBJECTIVE AND METHODS
The aim of the research is to perform quality control of the GNSS measurement results within the AGROS-RTK, using the methodology for setting up the geodetic basis. One of the ways to control quality is to do the measurements on a stable and reliable polygon in several time epochs. The measurements for setting up the geodetic basis are carried out according to the Professional Guidelines of the Republic Geodetic Authority [5]. All the calculations and tests for quality control purposes should be performed on the WGS84 ellipsoid, and in the reference framework of the AGROS network (ETRF2000), in the Cartesian orthogonal coordinates. The emphasis is placed on the control of the achieved results of the direct measurements, and accordingly, it is not necessary to make transformations in the plane of the state projection. Quality control of the obtained results is done by comparing several measurement epochs. The measurement plan envisages that, for duration of 30 seconds, with a 1 second interval of observation, the final coordinates for each point are obtained from each epoch. The estimation of coordinates for each measurement epoch is made according to the formulas [1]: The importance of deviation of coordinates can be determined by a statistical test of the equality of two values with known standards. The test is conducted with a probability of 95%, assuming that the measurements have a normal distribution [1]: Decision is made based on the hypothesis: where: q -quantile of normal distribution for the probability of 95%, g, r -ordinal numbers of the measurement epochs that are being tested.

Description of the experiment and the measurements
The polygon where the experiment was carried out is located on the territory of the cadastral municipality of Čajetina (CM Čajetina) located on the mountain of Zlatibor.
For the purpose of the experiment, all the necessary data of relevance were available. The basic satellite images were downloaded from public Internet portals [7] showing the position of points and the area of research (Figure 1).
The measurements were conducted using the GNSS (GPS) technology. The real-time kinematic positioning method (RTK) was used. The active geodetic reference network of the Republic of Serbia (AGROS network) was used as the basis.

Results
The estimation of definite coordinates was made for each measurement epoch separately.
The calculations were made in the Cartesian orthogonal coordinates on the WGS84 ellipsoid and in the reference framework of the AGROS network (ETRF2000).
The results of the definite coordinates are shown in Table 1. Differences of definite coordinates among the epochs are presented in the graph in Figure 2. Coordinates differences [cm]

Testing the point coordinates' matching
Statistical testing of the definite coordinates' matching among the measurement epochs was performed. The statistical test on the equality of two values with known standards was applied to the results at each measuring point, along all three coordinates. The test was carried out with a probability of 95%, assuming that the measurements had a normal distribution.
The results of testing the coordinates' differences are shown in Table 2.  Table 2 has the following meaning: 'TRUE' -statistically, in two tested epochs, the coordinates can be considered equal, 'FALSE' -statistically, in two tested epochs, the coordinates CANNOT be considered equal.

DISCUSSION AND CONCLUSION
Measurements for this research were carried out in three epochs with a time interval of one year. In each epoch, permanently stabilised points were observed, which were stable and invariant from other influences during the realisation of the experiment. The measurements were conducted according to the Professional Guidelines instructed by the Republic Geodetic Authority, which stipulate the proper use of the active geodetic basis of the Republic of Serbia. In all the measurement epochs, the same GNSS receiver was used, with a valid calibration certificate. Upon processing the measurement results and calculating definite coordinates for each measurement epoch, the coordinate differences among the epochs were calculated, in all the combinations. The differences are shown in Figure 3. Table 3 shows the range of the values of definite coordinates of the points in all the epochs.
By analysing the results from Table 3 and taking into account the accuracy of measurements, it was established that the coordinates among the epochs differ significantly. Statistical testing of equality of coordinates with known standards was carried out in all the combinations of the epochs. The testing results are presented in Table 2. Based on the obtained results it can be concluded that none of the geodetic points coordinates are matching in all the epochs of observation. The reasons for significant differences in the coordinates cannot be accurately determined on the basis of such an experiment. It is evident that all the effects that come from users and equipment are reduced to a minimum by using adequate and calibrated equipment, as well as by strict adherence to the Professional Guidelines for using the AGROS network. Further analysis of the causes could be directed to the quality of corrections distributed by the AGROS network or the quality of the data obtained from the satellite. Certainly, this could be the subject of some further research.