DETERMINATION OF THE PRECISE COORDINATES OF THE GPS REFERENCE STATION IN OF A GBAS SYSTEM IN THE AIR TRANSPORT

This paper presents results of research concerning determination of the GPS reference station coordinates located on the grounds of an EPDE airport in Deblin. The study uses a mathematical model of the PPP measurement technique in order to determine the coordinates of the reference station using the real GPS code-phase observations. The computations of the coordinates of the GPS reference station were carried out in numerical applications CSRS-PPP, APPS and GAPS. In this research was found that the accuracy of finding solutions to the XYZ geocentric coordinates of the reference station REF1 between solutions CSRS-PPP, APPS and GAPS ranges from 0.01 m to 0.13 m. In addition, the accuracy of determining the XYZ geocentric coordinates from the PPP method related to the GPS differential solution ranged from 0.01 m to 0.11 m.

construction of the GBAS system infrastructure is costly and time consuming and it requires appropriate training for air traffic control personnel. In Poland, the GBAS system is currently being implemented for Cracow Balice Airport [6].
According to ICAO, the GPS measurements in the area of an airport should be realized with accuracy better than 0.1 m. In addition, in the carrier phase DGPS technique, typical accuracy of the GPS navigation system is about 0.01÷0.05 m, whereas, in static measurements in the postprocessing mode, the GPS navigation system accuracy is around 0.01÷0.02 m [7]. The reference station coordinates in an airport must be estimated with the high level accuracy. In this way, the GPS reference station can be applied in conception of the GBAS technical infrastructure in the airport.
The aim of this article was to determine coordinates of the base station RTK GPS as one of the components of the GBAS augmentation system in the air transport. The precise coordinates of the RTK GPS reference station were determined using the PPP universal measurement technique for the GPS code-phase observations. The precise coordinates of the reference station REF1 were in calculations specified in the geocentric XYZ frame. A flight test was conducted for the reference station REF1, located within the military airport EPDE in Deblin.

Research method
The mathematical model of the GPS reference station coorrdinates determination is based on using the observation equations from the PPP measurement technique, as follows [8]:

Introduction
One of the elements of activating the GBAS augmentation system in air transport is the construction of a network of the RTK GPS permanent stations, located in the vicinity of both civil and military airports [1]. Ultimately, the GBAS augmentation system should consist of three components: the base station RTK GPS located at the airport, the mobile GPS receiver installed on board of an aircraft and transmission links of satellite data between the base station and the mobile receiver [2]. Such a configuration of components in the GBAS system ensures optimum utilization, during the precise positioning of an aircraft in the air transport. Within the GBAS augmentation system, it is possible to differentiate two basic methods of aircraft positioning: the DGPS differential technique and the RTK-OTF differential technique [3]. In the DGPS differential technique, the position of an aircraft is determined based on the GPS code observations, registered by the base station and the mobile receiver. On the other hand, in the RTK-OTF differential technique, the position of an aircraft is determined based on the GPS phase observations, registered by the base station and the mobile receiver [4].
The rules for the implementation and operation of the GBAS augmentation system in the air transport are clearly defined by the International Civil Aviation Organization ICAO [5]. In the framework of the ICAO guidelines and recommendations, the GBAS system finds its practical application in the procedure of a precision approach (PA) to landing. Among the types of a precision approach, it is possible to distinguish a precision approach, Category I, Category II and Category III. It is worth mentioning that the where: Sx-vector of searched parameters, A PPP -matrix of plan, P PPP -matrix of weights, C x -variance-covariance matrix of determined parameters in the XYZ geocentric frame in the PPP measurement technique, Cn -variance matrix of disturbances of the measurement process, lPPP -vector of constant terms.
In the stochastic process, in the PPP measurement technique, the determined parameters are modelled as [10]: • coordinates of the receiver of the GPS reference station as a constant value in the stochastic model, • receiver clock bias correction as a stochastic white noise model. • ZWD parameter as a stochastic model of a random walk, • phase uncertainty as a constant value in a stochastic model.

Research experiment
In the research experiment, the authors verified an application of the described research method in an accurate determination of coordinates of the reference station RTK GPS. In the analyzed example, coordinates of the reference station REF1 were determined, located at the military airfield in Deblin EPDE (see Figure 1). In test, the daily GPS observations data from REF1 GNSS station were applied, with time interval of 1 s. The experiment was realized on 1 st June 2010.
The research experiment exploited the GPS navigation data recorded by the Topcon HiperPro receiver, mounted at the reference station REF1 in Deblin. In particular, in this research the P1/P2 and phase L1/L2 code measurements in the GPS system were used. In the calculations, there was the PPP precise measurement technique was used in order to determine coordinates of the reference station REF1 in the XYZ geocentric frame. Within the conducted studies, the numerical calculations were made in three independent geodetic programmes, using the PPP measurement technique in order to determine the position of the GPS receiver in a static mode. In the calculations, the available free geodetic programmes were used: CSRS-PPP, APPS and GAPS [12].
For the purposes of the conducted numerical calculations, the configuration of the CSRS-PPP programme was set, as below: hcarrier frequencies in the GPS system, t -geometric distance between the GPS satellites and the receiver; it contains information about the parameters of the Earth's rotation, accurate coordinates of the satellite antenna and receiver, satellite antenna phase centre and receiver antenna phase centre, geodynamic and tidal effects, speed of the continental plate, etc. • mapping function of the tropospheric delay: Vienna mapping function.

Results and discussion
Findings of obtained results of the reference station REF1 coordinates, based on the CSRS-PPP, APPS and GAPS are shown in Tables 1, 2 and 3, respectively. Table 1 shows results of the X coordinate for the reference station REF1. The scatter of results of the X coordinate, for the reference station REF1, in the solution CSRS-PPP, APPS and GAPS, equals approximately ±0.02÷0.03 m. Table 2 shows the results of the Y coordinate for the reference station REF1. The scatter of results for the Y coordinate, for the reference station REF1, in the solution CSRS-PPP, APPS and GAPS, also equals approximately ± 0.02÷0.13 m. Table 3 shows results of the Z coordinate for the reference station REF1. The scatter of results for the Z coordinate, for the reference station REF1, in the solution CSRS-PPP, APPS and GAPS, also equals approximately ± 0.01÷0.06 m.
In Tables 4, 5 and 6 are presented the accuracy values in the form of standard deviations of determining the X, Y and Z coordinates of the reference station REF1, respectively. In Table 4 are shown results of the X coordinate mean values for the reference station REF1 in the CSRS-PPP, APPS and GAPS solution. The smallest value of the standard deviation for the X coordinate equals 0.01 m in the GAPS programme, whereas the largest one is equal to 0.03 m in the CSRS-PPP programme.
In Table 5 are presented results of the Y coordinate mean values for the reference station REF1 in the CSRS-PPP, APPS and GAPS solution. The smallest value of the standard deviation for the Y coordinate equals 0.02 m in the GAPS programme, whereas the largest one is equal to 0.07 m in the CSRS-PPP programme. In Table 6, there are results of mean values of the Z coordinate for the reference station REF1 in the CSRS-PPP, APPS and GAPS solution. The smallest value of the standard deviation for the Z coordinate equals 0.01 m in the GAPS programme, whereas the largest one is equal to 0.03 m in the CSRS-PPP programme.
Within the conducted experimental research, the authors verified the determined coordinates of the reference station REF1 in the PPP measurement technique. In the control test, the coordinate values of the reference station REF1, in the PPP measurement technique, were compared to the catalogue coordinates determined in the AUSPOS programme. In particular, the article compared the values of determined coordinates of the REF1 station in the geodetic XYZ frame. The catalogue coordinates of the REF1 reference station were determined in the AUSPOS programme. The programme AUSPOS ver. 2.2 is a free application tool to make computations of the GNSS receiver in a static mode, for the GPS phase observations [13]. The computational strategy for the determination of   The research method presented in this paper can be fully exploited in the creation of the GBAS system for development of the air transport. Therefore, it is justified to use the PPP measurement technique for accurate determination of coordinates of the GPS reference stations, installed at airports. Determined coordinates of the GPS reference station in the PPP measurement technique seem to be reliable and accurate in relation to the catalogue coordinates, calculated using the dualfrequency differentiation of the phase observations. It must be stressed that the GBAS system in Poland is at the stage of construction, which means that its particular components must be properly verified so that their quality should be the best possible in the age of development of aviation. In the future, the authors plan to perform further research tests on use of the PPP measurement technique in determining the GPS reference stations located in the vicinity of civil airports in Mielec and Chelm, in south-eastern Poland.

Acknowledgement
The authots would like to thanks for CSRS-PPP, APPS, GAPS and AUSPOS on-line service for numerical computations of research. This paper was supported by Polish Air Force University for 2020 year.
• for the Z coordinate: 4972325.87 m with the standard deviation of 0.02 m.
Owing to determination of the catalogue coordinates in the AUSPOS programme, it was possible to make a reliable evaluation of use of the PPP measurement technique in the static positioning. In particular, the verification process assesses the PPP positioning accuracy assessment in the GPS static mode. Based on that, it was possible to determine the difference in geocentric XYZ coordinates for the reference station REF1, as below [14]: where: , , dX dY dẐ h -parameters of accuracy positioning in the geocentric XYZ coordinates, Xi -the X coordinate of the reference station REF1 from the solution of the CSRS-PPP, APPS and GAPS, Yi -the Y coordinate of the reference station REF1 from the solution of the CSRS-PPP, APPS and GAPS, Zi -the Z coordinate of the reference station REF1 from the solution of the CSRS-PPP, APPS and GAPS, XAUSPOS -the X catalogue coordinate of the reference station REF1 from the AUSPOS solution, YAUSPOS -the Y catalogue of the reference station REF1, from the AUSPOS solution, ZAUSPOS -the Z catalogue coordinate of the reference station REF1 from the AUSPOS solution. Table 7 shows results of the GPS accuracy positioning for the reference station REF1. Based on the obtained comparative results from Equation (3), it can be concluded that the highest positioning accuracy by means of the PPP measurement technique is visible along the X axis, being equal to approximately ±0.01÷0.02 m. On the other hand, the lowest accuracy of the GPS positioning is noticeable along the Y axis, particularly in the case of the CSRS-PPP and GAPS solution. Along the Z axis, the GPS positioning accuracy equals ± 0.01÷0.04 m.

Conclusions
The article presents results of determination of accurate GPS coordinates of the GPS reference station as one of the GBAS augmentation system elements in the air transport. The GPS reference station coordinates