Polish Academy of Sciences [615934]

© Polish Academy of Sciences
DOI: 10.2478/geocart-2013-0014GEODESY AND CARTOGRAPHY
V ol. 62, No 2, 2013, pp. 217-233
Verifi cation of applicability of the Trimble RTX satellite technology
with xFill function in establishing surveying control networks
Robert Krzy żek
AGH University of Science and Technology,
Faculty of Mining Surveying and Environmental Engineering,
Department of Geomatics
30 Mickiewicza Al., 30-059 Krakow, Poland
e-mail: [anonimizat]
Received: 11 June 2013 / Accepted: 21 November 2013
Abstract: The paper presents the results of real time measurements of test geodetic
control network points using the RTK GPS and RTX Extended technologies. The Trimble RTX technology uses the xFill function, which enables real measurements without the need for constant connection with the ASG EUPOS system reference stations network. Comparative analyses of the results of measurements using the methods were performed and they were compared with the test control network data assumed to be error-free. Although the Trimble RTX technology is an innovative measurement method which is rarely used now, the possibilities it provides in surveying works, including building geodetic control networks, are satisfactory and it will certainly contribute to improving the organisation of surveying works.
Keywords: RTK GPS, RTX, Trimble xFill, geodetic control network
1. Introduction
In recent years, many scientists directed their research towards de fi nition of a new
(improved) Precise Point Positioning technique (PPP), as an alternative to RTK (Real Time Kinematic) based on permanent reference stations. The result of these activities was development of a new product on the surveying market, i.e. the RTX technology (Real Time eXtended). It is relies on the OmniSTAR system, which employs a constellation of telecommunication satellites and is based on a network of reference stations, located on different continents and using innovative algorithms for de fi ning
corrections for GNSS receivers (
www.geoforum.pl , 2013).
Most RTK systems are currently receiving corrections from a reference station by
radio or by mobile phone (via the Internet). The reference station in this case may be a single physical base station or a VRS (Virtual Station), data for which are generated by a network of receivers. Although the reference stations may be 40 to 70 kilometres apart, the VRS data are interpolated for a virtual, fi xed position near the rover. Figure
1 illustrates the two types of streams of RTK corrections (White Paper, 2012).
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Robert Krzyżek 218
Virtual Reference Station
(VRS) correction Physical Reference Station
correction
Fig. 1. Possible sources of corrections for most RTK systems: single physical reference station or VRS
(White Paper, 2012)
Physical Reference Station
correction
Fig. 2 RTK solution outage caused by a building obscuring the RTK radio signal
(White Paper, 2012)
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Verifi cation of usefulness of Trimble RTX satellite technology 219
The Trimble RTX with xFill function is a technology that supports the standard
RTK systems in case of outages of corrections from their primary source: a physical
reference station or a stream of VRS data.
A typical case of radio failure is shown in Figure 2, which illustrates loss of radio
signal caused by buildings. Signal fading takes place in areas, where a building is
located between the user and the reference station, effectively blocking the signal and causing the suspension of RTK positioning.
In the areas with satellite signal coverage the system Trimble RTX with the xFill
function determines position either with the data from a single base station or with data from a VRS station, as long as they are available, or the RTX data stream. In case of interruption of the reference signal (Fig. 2), the Trimble RTX system with the xFill function provides a mechanism for maintaining high precision RTK positioning based solely on GNSS observations collected by the rover. Using the RTX data, the moving receiver “ fi lls the gap” caused by the break of the original correction streams
– hence the name of the function xFill, see Figure 3 (White Paper, 2012).

Physical Reference Station
correction RTX L-band Satellite
Fig. 3. Expected behavior of the rover using the Trimble functions xFill (White Paper, 2012)
In result, when it comes to loss of corrections from reference stations, the Trimble
RTX data streams, transmitted by an independent link (RTX L – satellite band) instead of the base station radio or GPRS, are usually available. The terrestrial radio signals are sometimes blocked, though a good view of suf fi cient number of GNSS satellites
and access to the RTX data stream are still maintained. Under such circumstances the rover furnished with the xFill function is consistently able to deliver positions like in the RTK mode (White Paper, 2012).
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Robert Krzyżek 220
The new technology is provided by the RTXTM centerpoint positioning service,
which allows positioning with the accuracy at the level of single centimetres all over
the world in real time, without direct use of reference stations infrastructure. However, the main drawback of this technique is its relatively long convergence time required to achieve positioning with such accuracy. The convergence time is typically several dozen of minutes, but sometimes it may take up to several hours, depending on the geometry of satellite constellation, and weather conditions (Leonardo et al., 2011).
The RTX system operates on the basis of precise satellite information, generated
in data processing centres, as shown in Fig. 4.

Data from Stations
via Internet
NTRIP Caster Communication
Server
Orbit, Bias and Clock Processor Internet
GPRS
Trimble R10 L-band Satellite
Uplink Station
CMRx
Fig. 4. RTX technology system infrastructure overview
Data from monitoring stations located around the world are collected and
transmitted via the Internet to working centres located in various places. They are
also called operating centres (dashed red line in Figure 1), within which the reserve communication servers are used for processing and transferring data, such as precise parameters of satellite orbits, satellite clocks corrections and predictability of observation. Then, accurate satellite data are compressed in accordance with the CMRx message format. In the fi nal stage, the messages are sent to uplink stations or
made available to users through the Internet (Leonardo et al., 2011).
Requirements for satellite orbits used in the global RTX system consist primarily
of accuracy, continuity, solidity and reliability. Satellite positions should be accurate, but due to the fact, that real-time positions are computed using double differences
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Verifi cation of usefulness of Trimble RTX satellite technology 221
of phases, orbit have negligible impact on the determined rover positions. The
requirement of continuity is introduced to avoid the necessity of modelling observation inconsistencies in time. RTX network processors use a variety of techniques to control data in order to ensure their highest quality, when used for calculation of the fi nal products. Furthermore, reliability is a very important factor for real time data
processing. Currently orbit processors are able to work for several months with no intervention from operators while processing various events (Leonardo et al., 2011).
Determination of precise orbit parameters in the RTX
TM centerpoint system is
based on a combination of the Kalman fi lter for estimating the satellites position and
velocity, conditions of troposphere, the ambiguity resolution of phase measurements, solar radiation pressure parameters, harmonic coef fi cients of Earth gravity fi eld
and Earth orientation parameters. In this process, the problem of determination of integer phase ambiguities is resolved in real time. This means, that rover positions determined with help of the reference data, with basic systematic errors fi ltered out
thanks to the difference technique, after loss of the data link can still be determined with satisfactory accuracy, though for several minutes only.
Estimation of the satellite clock errors is the fundamental part of the RTX system,
which plays a vital role in positioning ef fi ciency. The speed of clock data processing
is important due to the fact, that assessment of clock errors is intimately related to the ambiguity resolution, so any delay in computation of these errors has direct impact on position determination. The architecture of the clock processor is based on an innovative design, that allows simultaneous processing of data from hundreds of the system reference stations. The aim is to make the time of processing of such data as short as much as possible, in order to facilitate 1 Hz positioning.
Effective approach to estimate clock errors has been presented by (Zhang
et al. (2011). It concerned a combined use of dual-thread algorithm consisting of undifferenced (UD) and epoch-differenced (ED) engine. The UD engine produces absolute clock values every 5 seconds, and the ED engine produces relative clock values between neighboring epochs in one – second interval. In the fi nal effect,
frequency of 1 Hz satellite clock can be obtained by combining the UD absolute clock values and the ED relative ones.
As mentioned before, one of the features of the RTX system is observation
predictability, which, when properly modelled, allow to achieve complete and accurate (to several centimetres) observations in GNSS. The main objective of generating such observations is to preserve the continuity requirement, which is introduced in order to avoid the possibility of inconsistent modeling at the time of observation.
During designing RTX system communications, a new message format was created
to transfer information on satellite orbits, clocks, observation predictability and other auxiliary information. The new format was based on earlier concepts developed by Trimble as part of the CMRx RTK format (Leonardo et al., 2011).
Positioning in the RTX technique has several technical aspects borrowed from
the previously existing RTK Trimble technique. This enables the RTX positioning mode to easily coexist with the traditional RTK modes. As far as the ef fi ciency of
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Robert Krzy żek 222
positioning is concerned, RTX performs typical positioning with accuracy to 1-2 cm
horizontally and 2-4 cm vertically. Final convergence of the system is achieved in 10 to 45 minutes from the start of the rover.
Convergence time may depend on various factors, including the geometry
of the satellite constellation or multipath properties of signals. In order to reduce convergence time in RTX positioning a range of functions are used. One of them is the so-called quick restart, which allows users, who have not made changes to their position from the last RTX solution, to immediately obtain a converged solution. The second feature is related to the avoidance of re-convergence system. This feature protects the system from entering a new phase of convergence in the case when the receiver loses connection to the satellites for a period of up to a few minutes, e.g. when working behind a line of trees or under a bridge (Leonardo et al., 2011).
Subsequent proposal aiming at reducing the convergence time is to use two
satellite systems GPS and GLONASS in the real-time measurements. A number of studies have shown that the solution of this type accelerates obtaining a convergent solution in comparison to works based on GPS only. Average time for the convergence of the system using GPS and GLONASS can be reduced by 42% (Zhang et al., 2013).
The RTX technology allows the use of the Trimble xFill
1 function, which allows
to continue surveying, even if the primary RTK or VRS correction stream is not available. This is made possible by providing access to the technology around the world by satellite broadband connections. The Trimble xFill function provides the possibility to use new and innovative techniques for RTK measurements (www.3dcad.pl, 2013). In the case of broken communication with the primary source of RTK or VRS corrections, the GPS receiver automatically switches to the RTX measuring mode with the Trimble xFill function. Theoretically (manufacturer’s data) working time in this mode may not exceed fi ve minutes. The new way of data processing is
different, competitive for the traditional solutions of the fi xed/ fl oat phase ambiguity.
It features uncertainty weighting, which allows for better error estimation compared to conventional GNSS solutions.
Surveying, including establishing of the surveying control network using the
RTK GPS technology, is currently regulated by the Ministry of the Interior’s and Administration Regulation of 9th November 2011 in case of technical standards of
performing detailed surveys and working out and sending results of these surveys to National Geodetic and Cartographic Store . Nevertheless, this regulation and
other previous guidelines do not regulate many other aspects related to real time measurements, or obligate to perform actions which do not always have to be done in accordance with the regulation to achieve the required accuracy. Due to the lack of clear legislation regulating the new measurement technology, i.e. RTX, the basic objective of the study was to analyse the results of measurements performed
1 Trimble xFill – a new service which continues RTK positioning for a few minutes when the RTK
correction stream is not available. Trimble X fi ll corrections are transmitted by satellites, so they are
generally available within the areas covered by the GNSS constellation (White Paper, 2012).
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Verifi cation of usefulness of Trimble RTX satellite technology 223
using the RTX technology with the Trible xFill function in relation to the legally
regulated RTK GPS technology. RTK GPS technology is one of the methods, that can be used to establish the surveying control network satisfying the requirements of the regulation (MIA, 2011). Confi rmation of relatively high accuracy of RTK GPS
method in the context of establishing surveying control networks, based not only on
the above mentioned regulation can be found in researches by (Krzy żek, et al., 2012).
Basing on the similarities of the RTK and RTX methods, the study also attempted to fi nd a link between the methods in the context of their mutual use to build the
surveying control network. The results may partly serve to moderate optimisation of measurement factors for the implementation of the surveying control networks using GNSS systems.
2. Research experiment
The test ground was located in the area of Jerzmanowie-Przeginia Commune in
vicinnity of Kraków, on an area of approximately 200 hectares. The study used a fragment of an existing control network of the class III (marked in accordance with the standard G-1), established and adjusted in 2005 (Fig. 5), documented in PODGiK (Provincial Geodetic and Cartographic Documentation Centre) in Krakow.
Fig. 5. Sketch of a fragment of the 3rd class detailed control network (test network)
in “Jerzmanowice-Przeginia” area
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Robert Krzy żek 224
The documentation shows, that the average error of adjusted point positions of the
tested geodetic control network did not exceed ± 0.003 m for horizontal coordinates and ±0.005 m for the vertical coordinate. Due to such high point position precision of the control network, coordinates of these points were taken as reference points – catalogue coordinates for further comparative analysis, and marked ”3
rd class CAT.”
in further determinations of coordinates. It should be noted, that coordinates of the reference points are not considered errorless, despite their low average error. The assumption of their values as a reference level to other research results is used in the context of comparison of the RTK or RTX surveyed positions to said data. The RTK and RTX methods achieve positioning accuracy on the level of several centimetres, so are substantially less accurate than the accepted reference ”catalogue” coordinates.
Trimble GNSS R10 receiver was used for real-time measurement of test points.
The measurements were performed using the ASG EUPOS system and the NAWGEO_VRS_2_3 service.
The system of permanent reference stations ASG-EUPOS-PL was put in operation
in Poland in the year 2008. Its main features, technical details and services of data distribution are given in the paper Technical details of establishing reference station
network ASG-EUPOS (Wajda et al., 2008). ASG EUPOS system with the use of
NAWGEO service assures accuracy of measurements in real time not worse than 3 cm for horizontal coordinates and less than 5 cm for heights with the con fi dence
level of 99.9% (www.asgeupos.pl, 2013). Veri fi cation of this assumption was carried
out and con fi rmed by (Uzna ński, 2010). Other researches carried out in the real time
using virtual reference stations (VRS) allow obtaining even better results than those mentioned above (Hu et al., 2003). Shortly after the launch of ASG EUPOS system tests on enhancing ef fi ciency of the real-time services have been started. To this end
a number of researches for the so-called ASG+ project have been done, which will support a number of modules for real-time measurements (Figurski et al., 2011).
Several scienti fi c and technical papers, pertaining to the operational aspects of the
system, were published in the last few years.
The location of the test area with respect to the nearest ASG-EUPOS stations is
shown on the Fig. 6.
Each test point was measured sequentially by two methods: RTK GPS and
Trimble RTX using xFill function. When surveying with the RTK GPS technique, the measurement mode was set to average the fi nal result from 30 epochs. On the other
hand, when using the RTX Trimble technology, the time interval in the measurements ranged from a few to a dozen or so seconds (most often 8 – 10 seconds), and was triggered by the observer. During measurements of points using the RTX with xFill technology, the possibility to continue measurements in time range given in the manufacturer’s data, was veri fi ed. In both methods the SurePoint technology was used,
thanks to which the range pole de fl ection was constantly monitored, what prevented
recording erroneous data and allowed recording only the data for which the pole was positioned vertically. The maximum allowed range pole de fl ection was set in the
receiver options to ± 0.010 m, while the allowed error of horizontal point position was
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Verifi cation of usefulness of Trimble RTX satellite technology 225
set also to ± 0.10 m, and the vertical position error to ±0.05 m. When any of these
thresholds was exceeded during the measurements, positioning was interrupted and further work was impossible.

Test object
Selected distances
Rover – KRA1: 19 km
Rover – KATO: 52 km
Rover – PROS: 38 km
Fig. 6. Arrangement of permanent stations ASG-EUPOS nearby municipalities Jerzmanowie-Przeginia
test (www.cgs.wat.edu.pl, 2013)
As a result of the research experiment, orthogonal coordinates X, Y , H in the
PL 2000 national system were determined for each measurement technology,
and a comparison was made. First, coordinates X, Y , H determined with the three methods were compared in pairs (RTK-RTX, RTK- 3rd class CAT., RTX-3rd class CAT.), what in result gave deviations dX, dY and dH for every coordinate of the test points (Table 1). Point number 1243 was excluded due to its signi fi cant damage. Point
number 1244 was totally excluded from the study due to the lack of measurement possibility using RTK and RTX, i.e. complete horizon obstruction from the south by a forested hill (Fig. 2). A null hypothesis was formulated for the obtained coordinate
deviations, which reads: the average value of μ for coordinate difference deviations
(dX, dY and dH) in individual pairs of methods (RTK-RTX; RTK- 3rd class CAT. and RTX – 3rd class CAT.) is equal to the set value μ
0 = 0.

0 0:P P H (1)
For the null hypothesis an alternative hypothesis was defi ned, which reads: the
average value of μ for coordinate difference deviations (dX, dY and dH) in individual
pairs of methods (RTK-RTX; RTK- 3rd class CAT. and RTX – 3rd class CAT.) does not equal the set value μ
0 ≠ 0.

0 1:P Pz H (2)
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Robert Krzy żek 226
Table. 1. Coordinates X, Y , H deviations between individual measurement technologies.
Point no.RTK-RTX [m] RTK-3rd class CAT. [m] RTX-3rd class CAT. [m]
dX dY dH dX dY dH dX dY dH
1220 -0.015 -0.001 -0.056 0.022 0.012 0.039 0.037 0.013 0.095
1234 -0.006 -0.007 0.020 -0.001 -0.037 0.037 0.005 -0.030 0.0171221 -0.014 0.001 0.003 0.022 -0.013 0.024 0.036 -0.014 0.0211224 0.003 -0.025 0.013 0.017 -0.036 0.015 0.014 -0.011 0.0021225 -0.018 -0.001 -0.012 0.060 0.006 0.020 0.078 0.007 0.032
1352 0.001 -0.004 0.007 0.008 -0.065 0.039 0.007 -0.061 0.032
1228 -0.003 -0.001 0.014 0.006 -0.005 -0.026 0.009 -0.004 -0.0401229 0.003 -0.006 0.001 0.000 -0.012 -0.043 -0.003 -0.006 -0.0441230 -0.021 -0.016 -0.045 0.039 0.017 0.012 0.060 0.033 0.0571231 0.012 0.010 0.044 0.027 -0.011 0.044 0.015 -0.021 0.0001232 -0.006 -0.001 0.000 0.028 0.002 0.061 0.034 0.003 0.0611233 -0.020 0.010 0.010 0.022 0.020 0.126 0.042 0.010 0.1161245 0.015 -0.002 -0.001 0.066 -0.050 -0.023 0.051 -0.048 -0.0221246 0.015 -0.041 -0.032 0.032 -0.050 -0.023 0.017 -0.009 0.0091247 -0.003 -0.004 -0.029 -0.041 -0.082 0.007 -0.038 -0.078 0.0361248 0.005 0.004 -0.015 0.081 0.011 0.060 0.076 0.007 0.0751249 -0.008 0.002 0.001 0.017 0.007 -0.010 0.025 0.005 -0.0111219 -0.003 0.004 -0.026 0.053 -0.024 0.037 0.056 -0.028 0.063
average value – μ -0.004 -0.004 -0.006 0.025 -0.017 0.022 0.029 -0.013 0.028
average deviation
– δ0.003 0.003 0.006 0.007 0.007 0.009 0.007 0.007 0.010
test model – T -1.3513 -1.5051 -1.0293 3.8248 -2.4314 2.3301 4.1742 -1.9823 2.6607
for signi fi cance
level of 5%
17 17 17 17 17 17 17 17 17 quantile k=n-1
critical valueof T- Student
distribution – t2.1098 2.1098 2.1098 2.1098 2.1098 2.1098 2.1098 2.1098 2.1098
Hypothesis
verifi cationH
0 H0 H0 H1 H1 H1 H1 H0 H1
In order to draw correct conclusions from the hypotheses tests, calculations of
the average value μ for coordinate difference deviations (dX, dY and dH) in each
individual set of methods were performed. The average value of standard deviation δ
was also calculated for the same data using the following formula:
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Verifi cation of usefulness of Trimble RTX satellite technology 227
nš
GPV (3)
where:
δ̂ – standard deviation of the deviations of coordinate differences (dX, dY , dH) in the
particular combinations of methods,
n – number of variations of coordinate differences (dX, dY , dH) in particular
combinations of methods.
Depending on the test sample (especially its volume), one of the three models of
the T test for the average value was used, expressed as follows:
PVPP
0 T (4)
For the average level of signi fi cance α=5% of k=n-1 degrees of freedom, the
variable T has the T-Student distribution. This distribution was used to construct a double-sided critical area, taking into consideration quantile t( α,k).
As a result of such an analysis of the test sample the following conclusions were
drawn:– average μ value for coordinate difference deviation (dX, dY , dH) between RTK
and RTX is statistically insigni fi cant, which generates no basis for rejecting the
hypothesis H
0,
– average μ value for coordinate difference deviation (dX, dY , dH) between RTK
and 3rd class CAT. and RTX and 3rd class CAT. is statistically signi fi cant, which
generates a basis for rejecting hypothesis H 0 in favour of hypothesis H 1.
The lack of ground to reject the hypothesis H 0 in comparison of the RTK and
RTX methods, allows for optimistic views on the possibilities provided by the xFill function in the Trimble RTX technology. Analysing the deviations of coordinates dX and dY one may notice slight differences, ranging from a few to a dozen or so mm (2 points above 20 mm) and slightly higher values for height deviations – from several to several dozen mm. The fact is, however, that basing on such analyses, far-fetched conclusions on the application of RTX (e.g. in establishing surveying control) cannot be drawn. Nevertheless, they render continuation of research in this fi eld justi fi ed. Further studies may present full veri fi cation of the accuracy of both
methods in certain time series (because of large volume of data, this issue will be presented in a separate publication).
Verifi cation of the proposed hypotheses, even though to a limited extent, de fi nitely
confi rms the known and legally regulated lack of possibility to establish detailed
control networks using real time GNSS techniques. Even though for deviations dY (Table 1) in the comparison of the RTX and 3rd class CAT. methods there is no basis for rejecting hypothesis H
0, a slight difference in the T test model of a single
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Robert Krzy żek 228
average value and the t of T-Student distribution should be noted. Assuming the
signi fi cance level α = 10% would lead to rejection of the hypothesis H 0 in favour of
the hypothesis H 1.
For the purpose of stronger con fi rmation of the alternative hypothesis, hence
rejecting the hypothesis H 0 in favour of the hypothesis H 1 (in the comparison of the
RTX and 3rd class CAT. methods) another comparison was made (Table 2). The table contains comparison of the coordinates X, Y , H only, between the methods for which the following null hypothesis was formulated: the average value of μ for coordinates
(X, Y, H) for the RTX – 3rd class CAT. equals the set value μ
0=0.
0 0:PP H (5)
For which an alternative hypothesis was de fi ned, which reads: the average value
of μ for coordinates (X, Y, H) for the RTX – 3rd class CAT. does not equal the set
value μ0≠0.
0 1:PPz H (6)
The average value of μ in the RTX method was determined basing on the
number of measurements made at each point. It should be noted, that due to the varied nature of the terrain (open horizon, obscured horizon, buildings) the period of successful measurement after switching to the RTX mode varied for some points, but never reached the time given by the manufacturer, i.e. fi ve minutes. As a result
of the variation of the time, the number of measurements made in the RTX mode was not the same at every point. A similar model of T test (model 4) of the single average value was de fi ned and the same level of signi fi cance α=5%. was adopted. In
this case, for formula 4, the μ value is the average value of coordinates X, Y , H of
each point measured using the RTX technology, and μ
0 is the value of coordinates
X, Y , H assumed to be error-free. Also in this analysis the T-Student distribution was used to construct a double-sided critical area, taking into consideration quantile t(α,k).
To sum up the results verifying the proposed hypotheses it may be said, that the
average value μ for coordinates (X, Y , H) for RTX-3rd class CAT does not equal
the set value μ
0≠0, which causes the rejection of the hypothesis H 0 in favour of the
hypothesis H 1. This conclusion con fi rms the dependences stemming from the proposed
alternative hypothesis for data in Table 1, i.e. between the results obtained from the
RTX method and the coordinates assumed to be error-free (3rd class CAT).
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Verifi cation of usefulness of Trimble RTX satellite technology 229Table. 2. Coordinates X, Y , H in individual measurement technologies
Point
no.RTX [m]no. of
measurm.
naverage stand. deviation 3rd class CAT. [m]Test model – T
for RTX – 3rd class CAT.sign.
lvl
5%critical
valueHypothesis
verifi cation
RTX – 3rd
class CAT.
XY H X Y H XY H X Y H XYH
1220 5564039.935 7410826.881 484.746 19 0.003 0.002 0.004 5564039.898 7410826.868 484.651 12.4298 6.5004 23.7165 18 2.1009 H1H1H1
1234 5563962.836 7410938.727 478.250 21 0.003 0.002 0.003 5563962.831 7410938.757 478.233 1.5204 -17.4571 5.5967 20 2.0860 H0H1H1
1221 5563543.024 7410615.189 484.397 18 0.003 0.002 0.004 5563542.988 7410615.203 484.376 13.3010 -5.8544 5.7161 17 2.1098 H1H1H1
1224 5563260.867 7410461.705 478.407 19 0.002 0.002 0.005 5563260.853 7410461.716 478.405 8.0527 -5.8364 0.3629 18 2.1009 H1H1H0
1225 5562935.088 7410403.601 480.122 19 0.003 0.002 0.004 5562935.010 7410403.594 480.090 28.1584 3.7985 8.8353 18 2.1009 H1H1H1
1352 5562655.489 7410408.624 468.903 16 0.002 0.001 0.003 5562655.482 7410408.685 468.871 3.0506 -47.3312 10.2800 15 2.1314 H1H1H1
1228 5562952.623 7410844.921 486.586 15 0.003 0.002 0.004 5562952.614 7410844.925 486.626 3.4540 -1.7461 -8.9872 14 2.1448 H1H0H1
1229 5563125.357 7411041.876 486.599 14 0.002 0.002 0.004 5563125.360 7411041.882 486.643 -1.4720 -3.6395 -10.6042 13 2.1604 H0H1H1
1230 5563229.651 7411122.286 483.745 14 0.003 0.003 0.005 5563229.591 7411122.253 483.688 20.8499 13.0550 11.4000 13 2.1604 H1H1H1
1231 5563430.588 7411301.150 475.406 11 0.003 0.002 0.006 5563430.573 7411301.171 475.406 5.7620 -8.9917 0.0599 10 2.2281 H1H1H0
1232 5563629.896 7411470.431 448.260 12 0.003 0.002 0.004 5563629.862 7411470.428 448.199 11.7649 1.4681 15.6712 11 2.2010 H1H0H1
1233 5563827.410 7411151.980 462.830 1 1meas. 1meas. 1meas. 5563827.368 7411151.970 462.714 0
1245 5563061.035 7412196.592 426.861 16 0.002 0.002 0.004 5563060.984 7412196.640 426.883 24.9848 -21.1402 -5.4841 15 2.1314 H1H1H1
1246 5562943.075 7412018.231 454.332 11 0.003 0.002 0.003 5562943.058 7412018.240 454.323 5.8740 -4.3033 2.7112 10 2.2281 H1H1H1
1247 5562904.953 7411841.824 452.739 19 0.005 0.002 0.005 5562904.991 7411841.902 452.703 -7.2538 -49.9090 7.3184 18 2.1009 H1H1H1
1248 5563056.425 7411466.766 476.245 19 0.002 0.002 0.003 5563056.349 7411466.759 476.170 34.4740 3.5328 24.3264 18 2.1009 H1H1H1
1249 5563109.938 7411248.798 486.259 12 0.004 0.002 0.004 5563109.913 7411248.793 486.270 5.9829 2.5079 -2.7215 11 2.2010 H1H1H1
1219 5564408.993 7411192.826 477.416 17 0.004 0.002 0.005 5564408.937 7411192.854 477.353 14.3165 -11.3926 12.9516 16 2.1199 H1H1H1
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Robert Krzyżek 230
To better illustrate the results of measurements in comparison between individual
methods, calculations of measured frequency of deviations (differences in coordinates)
in a set of linear intervals was performed. 18 common 5 mm long ranges for coordinate differences dX, dY , dH were prepared. They are presented below in the form of histograms (Fig. 7-9).
< -0.040
-0.040 ; -0.035
-0.035 ; -0.030
-0.030 ; -0.025
-0.025 ; -0.020
-0.020 ; -0.015
-0.015 ; -0.010
-0.010 ; -0.005
-0.005 ; 0.000
0.000 ; 0.005
0.005 ; 0.010
0.010 ; 0.015
0.015 ; 0.020
0.020 ; 0.025
0.025 ; 0.030
0.030 ; 0.035
0.035 ; 0.040
> 0.04001234567dX dY dH
Fig. 7. Histogram of measured frequency for differences in coordinates between
RTK-RTX methods< -0.040
-0.040 ; -0.035
-0.035 ; -0.030
-0.030 ; -0.025
-0.025 ; -0.020
-0.020 ; -0.015
-0.015 ; -0.010
-0.010 ; -0.005
-0.005 ; 0.000
0.000 ; 0.005
0.005 ; 0.010
0.010 ; 0.015
0.015 ; 0.020
0.020 ; 0.025
0.025 ; 0.030
0.030 ; 0.035
0.035 ; 0.040
> 0.040011223344
Fig. 8. Histogram of measured frequency for differences in coordinates between
RTK-3rd class CAT. methods
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Verifi cation of usefulness of Trimble RTX satellite technology 231< -0.040
-0.040 ; -0.035
-0.035 ; -0.030
-0.030 ; -0.025
-0.025 ; -0.020
-0.020 ; -0.015
-0.015 ; -0.010
-0.010 ; -0.005
-0.005 ; 0.000
0.000 ; 0.005
0.005 ; 0.010
0.010 ; 0.015
0.015 ; 0.020
0.020 ; 0.025
0.025 ; 0.030
0.030 ; 0.035
0.035 ; 0.040
> 0.0400123456
Fig. 9. Histogram of measured frequency for differences in coordinates between
RTX-3rd class CAT. methods
The above histograms clearly show the lack of normal distribution for the test
sample, which con fi rms that T-Student distribution should be used in the analysis. The
only coherence of the measurement results (in relation to the remaining histograms)
is visible in graphs for dX and dY in Figure 3. For dH in Figure 3 and the remaining differences in coordinates (dX, dY , dH) in Figures 4 and 5, measured frequency in the adopted ranges is stepwise incremental. For deviations dX, dY and dH presented in Figure 3, the highest likelihood of the occurrence of differences in coordinates between the RTX-RTX methods is ±0.005 m. For deviations dX, dY and dH showed in Figures 4 and 5 the highest likelihood of the occurrence of differences in coordinates between the RTK-3rd class CAT. methods and RTX-3rd class CAT. methods is higher or equal to the boundary value of the range ±0.040 m.
3. Conclusion
Although currently developed only to a limited extent, results of the research
experiment allow drawing fi rst conclusions on the employment of the Trimble RTX
with xFill function technology in low order control network building. Should the GPS
rover lose connection with RTK or VRS correction source, the measurement can be continued but with utmost care. Permanent supervision of measurement results, that is monitoring the values of vertical and horizontal errors on the controller screen, as well as time passed since the rover was disconnected from the reference station, allow determination and recording of proper and safe point coordinates of the network in real time using the RTX technology. It follows from the research, that the working
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Robert Krzy żek 232
time in RTX mode, given by the manufacturer, is longer than the actual time in
which RTX technology measurements can be made with the required accuracy. In reality, the time oscillates between 2 and 3.5 minutes. Vertical error of the measured point increases rapidly – two times faster than horizontal errors. Perhaps, if the RTX technology with xFill function were used only for determining X and Y coordinates of the geodetic control network, working time in this mode would equal to 5 minutes or might be even exceeded with the preservation of the required accuracy speci fi ed in
the regulation (MIA, 2011).
Summing up, the insights drawn from the results of research on the use of the
Trimble RTX with xFill function technology in establishing low order geodetic control show, that one might be optimistic about its possible employment in surveying. The technology gives more opportunities, when only horizontal positions of the control points are determined, while determination of spatial coordinates is limited to a shorter time. Conducting further research in the fi eld is well-grounded, as it will
allow veri fi cation of the real possibilities of employing the technology to establishing
local surveying control.
Acknowledgments
This work was carried out within the statutory studies of the AGH University of
Science and Technology, Faculty of Mining Surveying and Environmental Engineering No. 11.11.150.006.
References
Figurski M., Bogusz J., Bosy J., Kontny B., Krankowski A. & Wielgosz P . (2011). “ASG+”: project for
improving Polish multifunctional precise satellite positioning system. Reports on Geodesy , 2 (91),
51-58.
Hu G.R., Khoo H.S., Goh P.C. & Law C.L. (2003). Development and assessment of GPS virtual reference
stations for RTK positioning. Journal of Geodesy , 77 (5-6), 292-302.
Krzyżek R. & Skorupa B. (2012). Analysis of accuracy of determination of eccentric point coordinates
of the KRAW permanent geodetic station in RTK GPS measuring mode with the application of the NAWGEO service of the ASG-EUPOS system. Geomatics and Environmental Engineering , 6 (4),
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Leonardo R., Landau H., Nitschke M., Glocker M., Seeger S., Chen X., Deking A., Ben Tahar M.,
Zhang F., Ferguson K., Stolz R., Talbot M., Lu G., Allison T., Brandl M., Gomez V ., Cao W., Kipka A. & Trimble Terrasat GmbH, Germany. (2011). RTX Positioning: The next generation of cm-accurate Real-Time GNSS Positioning. White Paper_RTX.
MIA. (2011). Regulation of Minister of Interior and Administration – in case of technical standards
of performing detailed surveys and working out and sending results of these surveys to National Geodetic and Cartographic Database (in Polish). Journal of Laws of 2011 No. 263, entry 1572.
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Verifi cation of usefulness of Trimble RTX satellite technology 233
Wajda S., Oruba A. & Leo ńczyk M. (2008). Technical details of establishing reference station network
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Wery fi kacja przydatno ści technologii satelitarnej Trimble RTX
z funkcją xFill do zak ładania osnów pomiarowych
Robert Krzy żek
AGH Akademia Górniczo-Hutnicza
Wydział Geodezji Górniczej i In żynierii Środowiska
Katedra Geomatyki
al. A. Mickiewicza 30, 30-059 Kraków
e-mail: rkrzyzek@agh.edu.pl
Streszczenie
W pracy przedstawiono wyniki pomiarów w czasie rzeczywistym punktów osnowy testowej z wykorzy-
staniem technologii RTK GPS oraz RTX Extended. W technologii Trimble RTX wykorzystano funkcj ę
xFill, która daje mo żliwości realnego wykonywania pomiaru bez konieczno ści stałej łączności z siecią
stacji referencyjnych systemu ASG EUPOS. Wykonano analizy porównawcze wyników pomiaru mi ę-
dzy metodami oraz odniesiono je do danych osnowy testowej, przyj ętych za bezb łędne. Cho ć techno-
logia Trimble RTX jest innowacyjn ą metodą pomiaru i jeszcze rzadko stosowan ą, to możliwości jakie
daje w realizacjach prac geodezyjnych, w tym zak ładaniu osnów pomiarowych, s ą bardzo zadawalaj ące
i z pewno ścią przyczyni si ę do jeszcze lepszej i bardziej ekonomicznej organizacji prac geodezyjnych.
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