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Displacement monitoring performance of relative positioning and Precise Point Positioning (PPP) methods using simulation apparatus
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ScienceDirect Advances in Space Research xxx (2018) xxx–xxx www.elsevier.com/locate/asr
Displacement monitoring performance of relative positioning and Precise Point Positioning (PPP) methods using simulation apparatus Salih Alcay a,⇑, Sermet Ogutcu a, Ibrahim Kalayci a, Cemal Ozer Yigit b,c a
Department of Geomatics Engineering, Faculty of Engineering and Architecture, Necmettin Erbakan University, Konya, Turkey b School of Earth and Planetary Sciences, Curtin University, WA, Australia c Department of Geomatics Engineering, Faculty of Engineering, Gebze Technical University, Gebze, Turkey Received 11 June 2018; received in revised form 15 October 2018; accepted 2 November 2018
Abstract Besides the classical geodetic methods, GPS (Global Positioning System) based positioning methods are widely used for monitoring crustal, structural, ground etc., deformations in recent years. Currently, two main GPS positioning methods are used: Relative and Precise Point Positioning (PPP) methods. It is crucial to know which amount of displacement can be detected with these two methods in order to inform their usability according to the types of deformation. Therefore, this study conducted to investigate horizontal and vertical displacement monitoring performance and capability of determining the direction of displacements of both methods using a developed displacement simulator apparatus. For this purpose, 20 simulated displacement tests were handled. Besides the 24 h data sets, 12 h, 8 h, 4 h and 2 h subsets were considered to examine the influence of short time spans. Each data sets were processed using GAMIT/ GLOBK and GIPSY/OASIS scientific software for relative and PPP applications respectively and derived displacements were compared to the simulated (true) displacements. Then statistical significance test was applied. Results of the experiment show that using 24 h data sets, relative method can determine up to 6.0 mm horizontal displacement and 12.3 mm vertical displacement, while PPP method can detect 8.1 mm and 19.2 mm displacements in horizontal and vertical directions respectively. Minimum detected displacements are found to grow larger as time spans are shortened. Ó 2018 COSPAR. Published by Elsevier Ltd. All rights reserved.
Keywords: Displacement; GPS; Precise Point Positioning; Relative positioning
1. Introduction Deformation monitoring is a vital task in order to provide precautions and prevent economic loses and particularly loss of life. It is crucial to monitor structural and ground deformations caused by man-made failures and natural phenomena. Besides the traditional way of deformation monitoring using theodolite, total station, level etc., GPS technology plays a crucial role in deformation ⇑ Corresponding author.
E-mail address: [email protected] (S. Alcay).
monitoring and displacement determination in recent years, due to its highly automated, ease of use and less labor intensive. Two GPS positioning approaches generally implemented in order to achieve required accuracy for monitoring the deformations. Both methods have advantages and drawbacks compared to each other. While relative method requires minimum two GPS receiver, PPP is more cost effective method that requires stand-alone GPS receiver. Nevertheless, relative method provides more accurate positioning results (Yigit et al., 2016). Firuzabadı` and King (2012) showed that using sessions 6 h or longer and four
https://doi.org/10.1016/j.asr.2018.11.003 0273-1177/Ó 2018 COSPAR. Published by Elsevier Ltd. All rights reserved.
Please cite this article as: S. Alcay, S. Ogutcu, I. Kalayci et al., Displacement monitoring performance of relative positioning and Precise Point Positioning (PPP) methods using simulation apparatus, Advances in Space Research, https://doi.org/10.1016/j.asr.2018.11.003
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or more reference stations, the precision is typically 1– 2 mm in horizontal and about 3–5 mm in vertical. Gandolfi et al. (2017) examined the precision of PPP method and found that precision below 5 mm can be achieved using daily observations. According to the Bertiger et al. (2010), daily repeatability of PPP using GIPSY/OASIS software are found 2.8 mm and 6.0 mm for horizontal and vertical directions, respectively. Both methods have been used in many deformation monitoring applications including structural health monitoring (Yavasßoglu et al., 2018; Bao et al., 2018; Tang et al., 2017), seismic deformation monitoring (Tiryakioglu et al., 2017; Guo et al., 2012; Hefty and Gerhatova, 2012; Xu et al., 2013), land slide and subsidence monitoring (Xiao and He, 2013; Wang and Soler, 2015; Chatterjee et al., 2015) and crustal deformation monitoring (Vilayev et al., 2017; Ohta et al., 2008). Besides these studies Yigit et al. (2016) examined the potential of GPS PPP method for horizontal displacement monitoring. According to the results, using 24 h time spans, PPP can determine up to 1.5 cm horizontal displacement. Unlike Yigit et al. (2016), in this study, besides the horizontal monitoring performances of the relative and PPP methods, their vertical monitoring performances and minimum detectable deformation direction were also tested with larger data sets using scientific software. In order to determine which amount of displacement can be detectable using each method based on statistical test procedure, 24 h data sets and also 12 h, 8 h, 4 h, 2 h, subsets were employed. 2. Methodology Point displacements are determined on the basis of comparing point coordinates in two epochs (time). In this study
horizontal and vertical displacements are considered. A special apparatus which can simulate horizontal and vertical movements was devised and placed on the building of Necmettin Erbakan University, Engineering and Architecture Faculty. Fig. 1 shows the apparatus and the GPS receiver. The apparatus is able to move accurately in horizontal and vertical directions with a precision of 0.01 mm. Twenty simulated horizontal and vertical displacement tests (3, 7, 12, 18, 25, 33, 42, 52, 63, 75, 88, 102, 117, 133, 150, 168, 187, 207, 228, 250 mm) were conducted. The first horizontal and vertical displacements were set to 3 mm from the reference epoch, then displacements were increased by 1 mm for each day. Thus, the difference in the last two epoch was 22 mm (228–250 mm). Each horizontal and vertical displacement was evaluated between two consecutive epochs. In this way, tectonic motion can be safely ignored between the two consecutive epochs. Simulated displacement values between two consecutive epochs were taken as true displacements. 21 daily GPS data sets with one day interval from 173 to 220 day of the year (DOY) in 2017 were collected by Trimble Spectra Precision SP80 high-grade geodetic receiver. The reason for using one day interval is to get data sets from 0.00 to 24.00 UT. Except the first day, each day’s data were subdivided into mutually non-overlapping sessions as 12-8-4-2 h subsets. As a result, 21, 40, 60, 120 and 240 data sets were processed for the 24-, 12-, 8-, 4- and 2- hour time spans, respectively. Each data set was processed by GAMIT/ GLOBK and GIPSY/OASIS scientific software for relative and PPP methods, respectively. The displacement calculation from the processing was performed as follows; For each displacement test, the processed 24 h data of the previous day was taken as the reference epoch (initial
Fig. 1. Simulation apparatus and Spectra Precision SP80 GPS receiver.
Please cite this article as: S. Alcay, S. Ogutcu, I. Kalayci et al., Displacement monitoring performance of relative positioning and Precise Point Positioning (PPP) methods using simulation apparatus, Advances in Space Research, https://doi.org/10.1016/j.asr.2018.11.003
S. Alcay et al. / Advances in Space Research xxx (2018) xxx–xxx
position) and 24-12-8-4-2 data sets of the following days were processed using each software. Then, horizontalvertical displacement and azimuth angle from the reference epoch were computed for each data set as follows; pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð1Þ horizontal displacement ¼ north2 þ east2 vertical displacement ¼ up east azimuth angle ¼ atan north horizontal displacementresiduals
ð2Þ ð3Þ
¼ horizontal displacement true horizontal displacement
ð4Þ
vertical displacementresiduals ¼ vertical displacement true vertical displacement ð5Þ azimuthresiduals ¼ azimuth angle true azimuth angle
ð6Þ
Where, north, east and up are the resolved topocentric coordinates between the reference epoch and the processed 24-12-8-4-2 h data sets by each software, true horizontal_displacement and true_vertical_displacement stand for the simulated displacements between the two consecutive epochs, azimuth_angle is the computed azimuth angle between the two consecutive epochs, true_azimuth_angle represents the assumed true azimuth angle between the 24 h sessions of the first day (DOY 173) and 24 h sessions of the last day (DOY 220). Since true azimuth angle is constant along the horizontal displacement, the longer the baseline between the epochs, the less error in azimuth angle. 2.1. GAMIT/GLOBK processing strategy GAMIT/GLOBK is developed by Massachusetts Institute of Technology, incorporates double differencing approach (Herring et al. 2015) with single-baseline and network concept. GAMIT solution is not usually used to obtain the final coordinate estimate of the stations.
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GAMIT produces estimates and an associated covariance matrix of station positions with loose constraints on the parameters which are input to GLOBK. GLOBK uses Kalman filter to estimate final coordinates of the stations. There are two ways of reference frame realization in GAMIT/GLOBK. One way is finite constraints approach, applying the tight a priori uncertainties on the coordinates of one or more fiducial stations in GAMIT. This approach is rarely used, because it can distort the network if the assigned constraints are not represent for the real scenario. The second way is generalized constraints which minimizes the differences for the stabilization sites between the estimated coordinates in the solution and those given on the a priori, effectively translating and (optionally) rotating the estimated frame into the frame of the a priori coordinates with using glorg transformation (Herring et al. 2015). Table 1 summarizes the processing parameters used in this study. In this study, reference frame was realized based on five fiducial stations belonging to Turkish CORS Network (TUSAGA-Aktif) by using generalized constraints. Minimum and maximum baseline lengths between the fiducial stations and the rover are 63 km and 107 km, respectively. The assumed true measurement epoch coordinates of the fiducial stations were taken from their published values. Fig. 2 shows the location of fiducial stations and rover station. 2.2. GIPSY/OASIS processing strategy GIPSY/OASIS is developed by the NASA’s Jet Propulsion Laboratory (JPL). GIPSY/OASIS software applies single-receiver ambiguity resolution. The algorithm in GIPSY/OASIS processes dual-frequency GPS data from a single receiver together with wide-lane and phase bias estimates from the global network of GPS receivers that were used to generate the orbit and clock solutions for the GPS satellites (Bertiger et al., 2010). The algorithm performs double difference ambiguity resolution between the rover station and one of the stations in the network that
Table 1 GAMIT/GLOBK processing strategy. Elevation cut-off angle Weighting with elevation Epoch interval GNSS system Ephemerides Ionospheric effect Second order ionospheric effect Phase initial ambiguity Antex file Troposphere Troposphere gradients Code differential bias Reference frame realization Reference frame Solid Earth Tides
10 degree Applied 30 s GPS IGS precise ephemerides (Griffiths and Ray, 2015) Removed by L1, L2 linear combination Applied with using IONEX file Wide lane and narrow line combination IGS08.atx (Schmid et al. 2016) GPT2 model (Lagler et al. 2013) Computed Up to date DCB file (Wang et al. 2016) Generalized constraints with using GLOBK Igb08 (Griffiths and Ray, 2015) Applied (Watson et al., 2006)
Please cite this article as: S. Alcay, S. Ogutcu, I. Kalayci et al., Displacement monitoring performance of relative positioning and Precise Point Positioning (PPP) methods using simulation apparatus, Advances in Space Research, https://doi.org/10.1016/j.asr.2018.11.003
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Fig. 2. Location of the used stations.
were used to generate the orbit and clock solutions for the GPS satellites with using wide-lane and phase bias. For the details of the processing strategy of GIPSY/OASIS software, authors refer to Bertiger et al. (2010). Table 2 summarizes the processing parameters used in this study. 3. Significance testing of horizontal and vertical displacements Displacements were determined on the basis of comparing two epochs. Then null hypothesis and its alternative hypothesis were formed as follows ((7) and (8)); Table 2 GIPSY/OASIS processing strategy. Elevation cut-off angle Weighting with elevation Epoch interval GNSS system Ephemerides
Ionospheric effect Second order ionospheric effect Phase initial ambiguity Antex file Troposphere Troposphere gradients Code differential bias Reference frame Solid Earth Tides
10 degree Applied 30 s GPS FLINN precise ephemerides (JPL fiducial frame) (ftp://sideshow.jpl.nasa.gov/pub/ JPL_GPS_Products/Final/2018/) Removed by L1, L2 linear combination Applied with using IONEX file Wide lane and narrow line combination IGS08.atx (Schmid et al. 2016) GPT2 model (Lagler et al. 2013) Computed Up to date DCB file (Wang et al. 2016) Igb08 (Griffiths and Ray, 2015) Applied (Watson et al.,2006)
H 0 : EðdÞ ¼ 0 no displacement between two epochs
ð7Þ
H 0 : EðdÞ–0 displacement between two epochs
ð8Þ
Where 00 E00 represents ‘‘expected value”. The test statistic was computed as T Test ¼
d sim rmseðhorizontal=vertical=azimuth angleÞ
ð9Þ
and compared to the critical value ðT crit ) with a significance level of a. Where rms stands for root mean square error and computed using following Eq. (10), rffiffiffiffiffiffiffiffiffi ½VV ð10Þ RMSE ¼ n Where ‘‘v” stands for the differences between simulated (true) displacements and derived displacements. ‘‘n” is the number of obtained differences. In the test (9), it is possible to use standard deviation ‘‘r” instead of rms. Standard deviation values are calculated based on variancecovariance matrix and exhibits inner precision. However, the variance-covariance matrix derived from scientific software underestimates the magnitude of the error, mainly due to the fact that physical correlations are neglected (Kashani et al., 2004). The major goal of this study is to test the obtained results according to the true displacements. Therefore we used RMSE values which were computed based on true displacements. If T < T crit , the null hypothesis is accepted, otherwise (T > T crit Þ the null hypothesis is rejected. Details, regarding the critical value ðT crit ) including calculation procedure, formulations etc., authors refer to Savsˇek-Safic´ et al. (2006). As described in Savsˇek-Safic´ et al. (2006), the value of T crit is taken to be 3 as is used as a ‘‘rule of thumb”
Please cite this article as: S. Alcay, S. Ogutcu, I. Kalayci et al., Displacement monitoring performance of relative positioning and Precise Point Positioning (PPP) methods using simulation apparatus, Advances in Space Research, https://doi.org/10.1016/j.asr.2018.11.003
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which is larger than the value derived from distributed function of the test statistics. Therefore in this study, ‘‘3” was taken as critical value. 4. Results Computed displacements and azimuth angle between two consecutive epochs from each data set were assessed in terms of RMS error, minimum detectable displacement and azimuth angle. RMSEhorizontal
displacement
¼
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi X ffi horizontal displacement2residuals =n
ð11Þ
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r X ¼ vertical displacement2residuals =n
RMSEvertical
displacement
RMSEazimuth
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi X ¼ azimuth2residuals =n
ð12Þ
ð13Þ
Where, RMSEhorizontal displacement , RMSEvertical displacement and RMSEazimuth are the RMS errors of horizontal displacement, vertical displacement and azimuth angle, respectively. Outlier detection was applied using 3-sigma rule for displacements and azimuth angle (Lehmann, 2013; Klos et al., 2015). The results are given in the following subsections w.r.t. each method and data set. 4.1. Results of the processed data In this section, results of each data sets (24 h, 12 h, 8 h, 4 h, 2 h) including rms errors according to the formulas (11–13), outlier numbers, minimum detectable amount of displacement and azimuth angle according to the formula (9), minimum-maximum-mean values of residuals are given in the following tables. RMSE results based on 24 h observation illustrate that accuracy of the relative method is better than PPP method in horizontal-vertical directions and azimuth angle (Table 3). Residuals illustrate the differences between relative/PPP estimated displacements and simulated (true) displacements. Relative-estimated residuals range from 2.5 mm to 4.0 mm in the horizontal direction and
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7.3 mm to 9.9 mm in the vertical direction. PPP estimated residuals range between (4.6) mm – (5.7) mm and (11.1) mm – (11.6) mm in the horizontal and vertical directions, respectively. In addition, according to the test value (T Test ) and critical value ðT crit ), minimum detectable amount derived by relative method is 6.0 mm in the horizontal and 12.3 mm in the vertical directions. Minimum displacement detected by PPP method is 8.1 mm and 19.2 mm in horizontal and vertical directions, respectively. Moreover, in terms of minimum detectable azimuth angle based on relative method exhibits better results comparing to the PPP method. Besides Table 3, Fig. 3 illustrates the true displacements and relative-PPP estimated displacements for 24 h processing results. The other sessions are not given due to the size of the manuscript. Table 4 shows the results of relative and PPP methods based on 12 h observation. Horizontal and vertical results of both methods are close to the 24 h results. In terms of derived accuracy for horizontal-vertical displacements and azimuth angle, relative method produces better results comparing to the PPP. Minimum and maximum residuals of relative and PPP methods in horizontal direction range from 6.4 mm to 5.5 mm and -9.5 mm to 12.7 mm, respectively, whereas they reach in the order of cm level in vertical direction. In addition, RMSE of relative derived azimuth angle is approx. equal to the 24 h solutions. Minimum detected significant displacements by relative and PPP solutions are 7.2 mm and 13.8 mm in horizontal, 18.3 mm and 21.6 mm in vertical directions, respectively. Table 5 gives the details of both methods based on 8 h data processing. Accuracy of the relative-estimated horizontal displacements and azimuth angle are close to the 24 h and 12 h solutions. Nevertheless, RMSE of vertical displacement is a little larger (7.9 mm) comparing to the 24 h results. PPP-estimated RMSE values are close to the 24 and 12 h solutions in all components. It is possible to detect 8.4 mm and 13.8 mm horizontal displacements by relative and PPP methods, respectively. Minimum detectable amount of vertical displacement is 23.7 mm for relative method and 21.3 mm for PPP method. Table 6 shows statistical details of both methods based on 4 h results. While, RMSE values of relative and PPP methods in horizontal directions are 3.2 mm and 5.3 mm
Table 3 Statistical results of 24 h processing. RMSE
Outlier
Minimum detectable amount
Min residual
Max residual
Mean residual
Relative method Horizontal (mm) Vertical (mm) Azimuth angle (degree)
2.0 4.1 8.2
0 0 0
6.0 12.3 24.6
2.5 7.3 24
4.0 9.9 13
0.5 0.2 1.7
PPP method Horizontal (mm) Vertical (mm) Azimuth angle (degree)
2.7 6.4 13.4
0 0 1
8.1 19.2 40.2
4.6 11.1 41.4
5.7 11.6 48.5
0.6 0.5 2.0
Please cite this article as: S. Alcay, S. Ogutcu, I. Kalayci et al., Displacement monitoring performance of relative positioning and Precise Point Positioning (PPP) methods using simulation apparatus, Advances in Space Research, https://doi.org/10.1016/j.asr.2018.11.003
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Fig. 3. Displacement values of 24 h processing.
Table 4 Statistical results of 12 h processing. RMSE
Outlier
Minimum detectable amount
Min residual
Max residual
Mean residual
Relative method Horizontal (mm) Vertical (mm) Azimuth angle (degree)
2.4 6.1 7.9
0 0 1
7.2 18.3 23.7
6.4 10.5 23.3
5.5 16.3 19.2
0.6 2.3 1.1
PPP method Horizontal (mm) Vertical (mm) Azimuth angle (degree)
4.6 7.2 19.1
0 0 2
13.8 21.6 57.3
9.5 15.6 61.2
12.7 11.0 74.6
0.6 0.2 3.1
Table 5 Statistical results of 8 h processing. RMSE
Outlier
Minimum detectable amount
Min residual
Max residual
Mean residual
Relative method Horizontal (mm) Vertical (mm) Azimuth angle (degree)
2.8 7.9 9.5
0 1 2
8.4 23.7 28.5
4.4 11.2 32.9
6.4 25.6 19.2
1.1 3.5 2.1
PPP method Horizontal (mm) Vertical (mm) Azimuth angle (degree)
4.6 7.1 17.2
1 1 3
13.8 21.3 51.6
8.8 15.2 30.8
10.8 12.6 92.2
0.9 0.1 5.5
respectively, RMSE of vertical displacements is around 1 cm for both methods. Minimum significant horizontal displacement values detected by relative and PPP methods are 9.6 mm and 15.9 mm, respectively. However in the vertical direction minimum detectable amount is 30.0 mm for relative method and 30.6 mm for PPP method. In addition, the magnitude of minimum and maximum residuals are not exceed 10 mm and 15 mm in the horizontal direction,
33 mm and 28 mm in the vertical direction corresponding to relative and PPP methods, respectively. Associated with the maximum residuals of azimuth angle minimum detectable amount of PPP is worse than the relative derived azimuth angle. For 2 h processing, the outlier numbers and maximumminimum residuals are larger than that of the other data sets (Table 7). Minimum and maximum residuals are in
Please cite this article as: S. Alcay, S. Ogutcu, I. Kalayci et al., Displacement monitoring performance of relative positioning and Precise Point Positioning (PPP) methods using simulation apparatus, Advances in Space Research, https://doi.org/10.1016/j.asr.2018.11.003
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Table 6 Statistical results of 4 h processing. RMSE
Outlier
Minimum detectable amount
Min residual
Max residual
Mean residual
Relative method Horizontal (mm) Vertical (mm) Azimuth angle (degree)
3.2 10.0 15.1
1 2 2
9.6 30.0 45.3
7.5 17.3 50.1
9.9 32.2 47.7
1.0 3.5 2.7
PPP method Horizontal (mm) Vertical (mm) Azimuth angle (degree)
5.3 10.2 21.0
1 2 4
15.9 30.6 63.0
11.3 22.6 89.5
15.0 27.3 74.0
1.2 0.1 3.2
Table 7 Statistical results of 2 h processing. RMSE
Outlier
Minimum detectable amount
Min residual
Max residual
Mean residual
Relative method Horizontal (mm) Vertical (mm) Azimuth angle (degree)
4.2 14.1 23.9
8 4 8
12.6 42.3 71.7
12.9 45.1 71.7
19.1 50.8 88.6
1.3 3.6 1.5
PPP method Horizontal (mm) Vertical (mm) Azimuth angle (degree)
5.9 13.7 27.2
1 4 9
17.7 41.1 81.6
13.4 43.1 103.3
17.8 45.8 120.9
1.7 0.4 0.5
the order of cm level for horizontal-vertical directions. Minimum horizontal displacement detected by relative method and PPP solutions are 12.6 mm and 17.7 mm, respectively. However in the vertical direction minimum detectable amount is 42.3 mm for relative method and 41.1 mm for PPP. As it is shown from the Tables 3–7, mean residuals of vertical components corresponding to relative method are worse than the PPP method. This shows that systematic errors in vertical component of PPP are less than the relative method in this study. In order to investigate the possible reasons of outliers and high residuals for 2 h sessions, ambiguity resolution, ionospheric condition and meteorological events were examined. In order to see whether there is any ionospheric activity during the collection of GPS data, geomagnetic storm (kp), geomagnetic activity (Dst) and solar activity (F10.7) indices were examined. According to the indice values, no ionospheric storm was detected during the data collection period. However, it is observed that ambiguity resolution and wet tropospheric delay play a significant role. Low percentage of narrow lane ambiguity resolution
is the main reason of outliers and high residuals among the data sets. Some outliers and high residuals in horizontal and vertical components for 2 h sessions are induced by the meteorological events known as thunderstorm and heavy rain. Table 8 shows the derived outliers/residuals and ambiguity resolution for each method during the meteorological events. As given in Table 8, there are thunderstorms between 10 and 12 UT on DOY 179, 215 and heavy rain 18-20 UT on DOY 215. The largest outlier is observed as 22.1 cm in vertical direction on DOY 179, 10-12 UT based on relative method. In addition, ambiguity resolution is rather low for both methods. The main reason for low narrow-lane ambiguity resolution is due to the noise of the code data. Table 9 shows the statistics of ambiguity resolutions for 2 h non-outlier observations. Compared to the Table 8 and Table 9, it is seen that meteorological events mostly effect the ambiguity resolution. Fig. 4 depicts the positive (yellow) and negative residuals (green) of one-way (un-differenced) ionosphere-free linear phase combination for each satellite-station pair for
Table 8 Outliers related to meteorological events. Software
Time interval
Horizontal outliers/residuals (cm)
Vertical outliers (cm)
Ambiguity resolution
Meteorological event
Relative Method PPP Method Relative Method PPP Method Relative Method PPP Method
10–12 10–12 10–12 10–12 18–20 18–20
5.3 1.3 1.5 3.4 0.05 0.4
22.1 10.8 9.8 9.4 2.6 4.3
19% 53% 39% 28% 71% 42%
Thunderstorm Thunderstorm Thunderstorm Thunderstorm Heavy rain Heavy rain
(DOY:179) (DOY:179) (DOY:215) (DOY:215) (DOY:215) (DOY:215)
(Narrow-lane) (Wide-narrow lane) (Narrow-lane) (Wide-narrow lane) (Narrow-lane) (Wide-narrow lane)
Please cite this article as: S. Alcay, S. Ogutcu, I. Kalayci et al., Displacement monitoring performance of relative positioning and Precise Point Positioning (PPP) methods using simulation apparatus, Advances in Space Research, https://doi.org/10.1016/j.asr.2018.11.003
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Table 9 Statistics of ambiguity resolution.
4.2. Differences according to the accuracy thresholds
Statistics (relative method) Minimum Maximum Mean
Ambiguity resolution (narrow-lane) 57% 100% 89%
Statistics (PPP method) Minimum Maximum Mean
Ambiguity resolution (wide-narrow lane) 61% 90% 72%
Besides the maximum-minimum differences and RMSE values which are given in the previous subsection, a set of thresholds were specified in order to examine the percentage of the residuals according to their magnitudes. Tables 10 and 11 give the thresholds of the horizontal and vertical differences, respectively, according to observation times spanning long to short data lengths. From Table 10, it is apparent that the magnitude of data according to the thresholds for both methods improves as the observation time increases. Based on the longest (24 h) and shortest (2 h) observation periods, most of the horizontal residuals (50%) are between 1 and 3 mm for both methods. In terms of the number of magnitudes and their thresholds, relative method provides better results comparing to the PPP. Furthermore, even in the shortest time span (2 h), the differences did not exceed 13–20 mm threshold values by two methods. Table 11 depicts the thresholds of vertical differences based on relative and PPP methods. In terms of the magnitudes, vertical differences are higher than the horizontal differences. Although there is no residuals larger than 20 mm even for the 2 h results in horizontal direction, 4.2% and 5.1% of 2 h vertical residuals are larger than 30 mm based on relative and PPP methods, respectively. Similar to the horizontal values, the superiority of the relative method over PPP method are distinguished in terms of vertical values. In addition, it is possible to observe the influence of observation duration more clearly comparing to the horizontal results.
each measurement epoch after the adjustment. These residuals contain non-modelled error sources such as multipath, water vapor and higher-order ionospheric delay. Since higher-order ionospheric effect (up to second order) is modelled in both relative and PPP techniques, the remaining residuals mainly indicate the multipath, wet delay and phase noise. Positive residuals mean the observed phase is more delayed than the modelled phase, while negative residuals mean the observed phase is less delayed than modelled one after the adjustment. Since the phase multipath of the test station is theoretically constant, the relatively large amount of residuals in the sky plot for DOY 179 could be interpreted as the relatively large amount of wet delay compared to DOY 181. The plot was created using GAMIT/GLOBK software. As depicted in Fig. 5, the wet delay changes in DOY 179 10-12 UT are more fluctuated compared to DOY 181. This would be the main reason for the largest vertical outlier among the data sets.
Fig. 4. Positive and negative phase residuals for each arch of GPS satellites for DOY 179, 181 (10-12 UT), the red bar in the plots is scale (10 mm). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Please cite this article as: S. Alcay, S. Ogutcu, I. Kalayci et al., Displacement monitoring performance of relative positioning and Precise Point Positioning (PPP) methods using simulation apparatus, Advances in Space Research, https://doi.org/10.1016/j.asr.2018.11.003
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Fig. 5. Changes of wet zenith tropospheric delay for DOY 179, 181 (10-12 UT).
Table 10 Thresholds of horizontal differences. Threshold of Dif. (mm)
0–1
1–3
3–5
5–8
8–13
13–20
20–30
30-
Relative method (horizontal) 24 h (%) 12 h (%) 8 h (%) 4 h (%) 2 h (%)
40.0 32.5 20.0 27.7 23.7
50.0 52.5 51.7 42.9 34.1
10.0 10.0 23.3 14.3 22.4
5.0 5.0 13.4 14.7
1.7 4.3
0.9
PPP method (horizontal) 24 h (%) 12 h (%) 8 h (%) 4 h (%) 2 h (%)
20.0 10.0 8.5 11.8 13.0
50.0 30.0 32.2 23.5 28.0
25.0 37.5 33.9 30.3 19.7
5.0 17.5 18.6 22.7 21.8
5.0 6.8 9.2 15.1
2.5 2.5
Threshold of Dif. (mm)
0–1
1–3
3–5
5–8
8–13
Relative method (vertical) 24 h (%) 12 h (%) 8 h (%) 4 h (%) 2 h (%)
13–20
20–30
30-
25.0 12.5 8.5 11.9 5.5
40.0 35.0 25.4 12.7 14.8
10.0 15.0 20.3 16.1 11.0
20.0 20.0 22.0 16.1 20.3
5.0 12.5 10.2 22.0 18.2
5.0 11.9 18.6 13.6
1.7 1.7 12.3
0.8 4.2
PPP method (vertical) 24 h (%) 12 h (%) 8 h (%) 4 h (%) 2 h (%)
5.0 7.5 15.3 11.9 5.9
30.0 17.5 13.6 13.6 12.3
15.0 17.5 22.0 8.5 16.5
20.0 22.5 23.7 23.7 15.3
30.0 30.0 18.6 22.9 24.6
5.0 6.8 13.6 11.4
5.9 8.9
5.1
Table 11 Thresholds of vertical differences.
5. Conclusions This study was conducted to evaluate the displacement monitoring performance of relative and PPP methods in horizontal and vertical directions. Analysis based on
24 h, 12 h, 8 h observation durations for both methods reveals high consistency to determine true displacements in horizontal direction. However vertical displacement residuals are a little larger comparing to the horizontal results for all data sets (24 h-2 h). The superiority of the rel-
Please cite this article as: S. Alcay, S. Ogutcu, I. Kalayci et al., Displacement monitoring performance of relative positioning and Precise Point Positioning (PPP) methods using simulation apparatus, Advances in Space Research, https://doi.org/10.1016/j.asr.2018.11.003
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ative method over PPP is observed particularly in the horizontal direction. In terms of minimum detectable horizontal displacements, while relative method provides better than 1 cm even based on 4 h processing, PPP method requires long time span to reach similar amount of minimal detectable displacements (24 h). However, both methods cannot provide better than 1 cm in the vertical direction even using 24 h observation. In this study, direction of the deformation also computed using azimuth angle. It is observed that if the displacement between two points are large enough, direction of the deformation can be computed accurately. Since the used distance is too short for the determination of azimuth direction (25 cm), the obtained accuracy is relatively low. However, it is important to illustrate the superiority of the relative method over PPP for deformation direction. The significance of the experiment indicates that besides relative positioning method, PPP method can be used in many deformation monitoring applications including seismic event, landslide, structure etc., depending on the displacement monitoring performance. The authors recommend that in order to obtain reliable results during the displacement monitoring period and analysis, meteorological events and ambiguity resolution should be taken into consideration. Acknowledgements This study was funded by the Scientific Research Projects Grant of Necmettin Erbakan University (Project No: 161219013).The authors would like to express their gratitude to NASA Jet Propulsion Laboratory (JPL) and Massachusetts Institute of Technology (MIT) for providing GIPSY/OASIS and GAMIT/GLOBK scientific software. The authors would like to thank to Dr. Huseyin Zahit Selvi for designing Fig. 2 using GMT. The fourth author is awarded a grant by The Scientific and Technological Research Council of Turkey (TUBITAK) to perform a research on High-rate GNSS-PPP Method for GNSS seismology and Structural Health Monitoring Applications at School of Earth and Planetary Sciences, Curtin University, Australia. He would like to thank TUBITAK, Science fellowships and Grant Programs Department for the support. The authors also thank to the reviewers for their reviews, critical comments and helpful suggestions, which improved the manuscript greatly. References Bao, Y., Guo, W., Wang, G., Gan, W., Zhang, M., Shen, J., 2018. Millimeter-Accuracy structural deformation monitoring using standalone GPS: Case study in Beijing, China. J. Surv. Eng. 144 (1). https:// doi.org/10.1061/(ASCE)SU.1943-5428.0000242. Bertiger, W., Desai, S.D., Haines, B., Harvey, N., Moore, A.W., Owen, S., Weiss, J.P., 2010. Single receiver phase ambiguity resolution with GPS data. J. Geod. 84 (5), 327–337. Chatterjee, R.S., Thapa, S., Sıngh, K.B., Varunakumar, G., Raju, E.V.R., 2015. Detecting, mapping and monitoring of land subsidence in Jharia Coalfield, Jharkhand, India by spaceborne differential interferometric
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Yavasßoglu, H.H., Kalkan, Y., Tiryakioglu, I., Yigit, C.O., Ozbey, V., Alkan, M.N., Bilgi, S., Alkan, R.M., 2018. Monitoring the deformation and strain analysis on the Ataturk Dam, Turkey. Geomatics Nat. Hazards Risk 9 (1), 94–107. https://doi.org/10.1080/ 19475705.2017.1411400. Yigit, C.O., Coskun, M.Z., Yavasoglu, H., Arslan, A., Kalkan, Y., 2016. The potential of GPS Precise Point Positioning method for point displacement monitoring: A Case Study. Measurement 91, 398–404. https://doi.org/10.1016/j.measurement.2016.05.074.
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ScienceDirect Advances in Space Research xxx (2018) xxx–xxx www.elsevier.com/locate/asr
Displacement monitoring performance of relative positioning and Precise Point Positioning (PPP) methods using simulation apparatus Salih Alcay a,⇑, Sermet Ogutcu a, Ibrahim Kalayci a, Cemal Ozer Yigit b,c a
Department of Geomatics Engineering, Faculty of Engineering and Architecture, Necmettin Erbakan University, Konya, Turkey b School of Earth and Planetary Sciences, Curtin University, WA, Australia c Department of Geomatics Engineering, Faculty of Engineering, Gebze Technical University, Gebze, Turkey Received 11 June 2018; received in revised form 15 October 2018; accepted 2 November 2018
Abstract Besides the classical geodetic methods, GPS (Global Positioning System) based positioning methods are widely used for monitoring crustal, structural, ground etc., deformations in recent years. Currently, two main GPS positioning methods are used: Relative and Precise Point Positioning (PPP) methods. It is crucial to know which amount of displacement can be detected with these two methods in order to inform their usability according to the types of deformation. Therefore, this study conducted to investigate horizontal and vertical displacement monitoring performance and capability of determining the direction of displacements of both methods using a developed displacement simulator apparatus. For this purpose, 20 simulated displacement tests were handled. Besides the 24 h data sets, 12 h, 8 h, 4 h and 2 h subsets were considered to examine the influence of short time spans. Each data sets were processed using GAMIT/ GLOBK and GIPSY/OASIS scientific software for relative and PPP applications respectively and derived displacements were compared to the simulated (true) displacements. Then statistical significance test was applied. Results of the experiment show that using 24 h data sets, relative method can determine up to 6.0 mm horizontal displacement and 12.3 mm vertical displacement, while PPP method can detect 8.1 mm and 19.2 mm displacements in horizontal and vertical directions respectively. Minimum detected displacements are found to grow larger as time spans are shortened. Ó 2018 COSPAR. Published by Elsevier Ltd. All rights reserved.
Keywords: Displacement; GPS; Precise Point Positioning; Relative positioning
1. Introduction Deformation monitoring is a vital task in order to provide precautions and prevent economic loses and particularly loss of life. It is crucial to monitor structural and ground deformations caused by man-made failures and natural phenomena. Besides the traditional way of deformation monitoring using theodolite, total station, level etc., GPS technology plays a crucial role in deformation ⇑ Corresponding author.
E-mail address: [email protected] (S. Alcay).
monitoring and displacement determination in recent years, due to its highly automated, ease of use and less labor intensive. Two GPS positioning approaches generally implemented in order to achieve required accuracy for monitoring the deformations. Both methods have advantages and drawbacks compared to each other. While relative method requires minimum two GPS receiver, PPP is more cost effective method that requires stand-alone GPS receiver. Nevertheless, relative method provides more accurate positioning results (Yigit et al., 2016). Firuzabadı` and King (2012) showed that using sessions 6 h or longer and four
https://doi.org/10.1016/j.asr.2018.11.003 0273-1177/Ó 2018 COSPAR. Published by Elsevier Ltd. All rights reserved.
Please cite this article as: S. Alcay, S. Ogutcu, I. Kalayci et al., Displacement monitoring performance of relative positioning and Precise Point Positioning (PPP) methods using simulation apparatus, Advances in Space Research, https://doi.org/10.1016/j.asr.2018.11.003
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or more reference stations, the precision is typically 1– 2 mm in horizontal and about 3–5 mm in vertical. Gandolfi et al. (2017) examined the precision of PPP method and found that precision below 5 mm can be achieved using daily observations. According to the Bertiger et al. (2010), daily repeatability of PPP using GIPSY/OASIS software are found 2.8 mm and 6.0 mm for horizontal and vertical directions, respectively. Both methods have been used in many deformation monitoring applications including structural health monitoring (Yavasßoglu et al., 2018; Bao et al., 2018; Tang et al., 2017), seismic deformation monitoring (Tiryakioglu et al., 2017; Guo et al., 2012; Hefty and Gerhatova, 2012; Xu et al., 2013), land slide and subsidence monitoring (Xiao and He, 2013; Wang and Soler, 2015; Chatterjee et al., 2015) and crustal deformation monitoring (Vilayev et al., 2017; Ohta et al., 2008). Besides these studies Yigit et al. (2016) examined the potential of GPS PPP method for horizontal displacement monitoring. According to the results, using 24 h time spans, PPP can determine up to 1.5 cm horizontal displacement. Unlike Yigit et al. (2016), in this study, besides the horizontal monitoring performances of the relative and PPP methods, their vertical monitoring performances and minimum detectable deformation direction were also tested with larger data sets using scientific software. In order to determine which amount of displacement can be detectable using each method based on statistical test procedure, 24 h data sets and also 12 h, 8 h, 4 h, 2 h, subsets were employed. 2. Methodology Point displacements are determined on the basis of comparing point coordinates in two epochs (time). In this study
horizontal and vertical displacements are considered. A special apparatus which can simulate horizontal and vertical movements was devised and placed on the building of Necmettin Erbakan University, Engineering and Architecture Faculty. Fig. 1 shows the apparatus and the GPS receiver. The apparatus is able to move accurately in horizontal and vertical directions with a precision of 0.01 mm. Twenty simulated horizontal and vertical displacement tests (3, 7, 12, 18, 25, 33, 42, 52, 63, 75, 88, 102, 117, 133, 150, 168, 187, 207, 228, 250 mm) were conducted. The first horizontal and vertical displacements were set to 3 mm from the reference epoch, then displacements were increased by 1 mm for each day. Thus, the difference in the last two epoch was 22 mm (228–250 mm). Each horizontal and vertical displacement was evaluated between two consecutive epochs. In this way, tectonic motion can be safely ignored between the two consecutive epochs. Simulated displacement values between two consecutive epochs were taken as true displacements. 21 daily GPS data sets with one day interval from 173 to 220 day of the year (DOY) in 2017 were collected by Trimble Spectra Precision SP80 high-grade geodetic receiver. The reason for using one day interval is to get data sets from 0.00 to 24.00 UT. Except the first day, each day’s data were subdivided into mutually non-overlapping sessions as 12-8-4-2 h subsets. As a result, 21, 40, 60, 120 and 240 data sets were processed for the 24-, 12-, 8-, 4- and 2- hour time spans, respectively. Each data set was processed by GAMIT/ GLOBK and GIPSY/OASIS scientific software for relative and PPP methods, respectively. The displacement calculation from the processing was performed as follows; For each displacement test, the processed 24 h data of the previous day was taken as the reference epoch (initial
Fig. 1. Simulation apparatus and Spectra Precision SP80 GPS receiver.
Please cite this article as: S. Alcay, S. Ogutcu, I. Kalayci et al., Displacement monitoring performance of relative positioning and Precise Point Positioning (PPP) methods using simulation apparatus, Advances in Space Research, https://doi.org/10.1016/j.asr.2018.11.003
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position) and 24-12-8-4-2 data sets of the following days were processed using each software. Then, horizontalvertical displacement and azimuth angle from the reference epoch were computed for each data set as follows; pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð1Þ horizontal displacement ¼ north2 þ east2 vertical displacement ¼ up east azimuth angle ¼ atan north horizontal displacementresiduals
ð2Þ ð3Þ
¼ horizontal displacement true horizontal displacement
ð4Þ
vertical displacementresiduals ¼ vertical displacement true vertical displacement ð5Þ azimuthresiduals ¼ azimuth angle true azimuth angle
ð6Þ
Where, north, east and up are the resolved topocentric coordinates between the reference epoch and the processed 24-12-8-4-2 h data sets by each software, true horizontal_displacement and true_vertical_displacement stand for the simulated displacements between the two consecutive epochs, azimuth_angle is the computed azimuth angle between the two consecutive epochs, true_azimuth_angle represents the assumed true azimuth angle between the 24 h sessions of the first day (DOY 173) and 24 h sessions of the last day (DOY 220). Since true azimuth angle is constant along the horizontal displacement, the longer the baseline between the epochs, the less error in azimuth angle. 2.1. GAMIT/GLOBK processing strategy GAMIT/GLOBK is developed by Massachusetts Institute of Technology, incorporates double differencing approach (Herring et al. 2015) with single-baseline and network concept. GAMIT solution is not usually used to obtain the final coordinate estimate of the stations.
3
GAMIT produces estimates and an associated covariance matrix of station positions with loose constraints on the parameters which are input to GLOBK. GLOBK uses Kalman filter to estimate final coordinates of the stations. There are two ways of reference frame realization in GAMIT/GLOBK. One way is finite constraints approach, applying the tight a priori uncertainties on the coordinates of one or more fiducial stations in GAMIT. This approach is rarely used, because it can distort the network if the assigned constraints are not represent for the real scenario. The second way is generalized constraints which minimizes the differences for the stabilization sites between the estimated coordinates in the solution and those given on the a priori, effectively translating and (optionally) rotating the estimated frame into the frame of the a priori coordinates with using glorg transformation (Herring et al. 2015). Table 1 summarizes the processing parameters used in this study. In this study, reference frame was realized based on five fiducial stations belonging to Turkish CORS Network (TUSAGA-Aktif) by using generalized constraints. Minimum and maximum baseline lengths between the fiducial stations and the rover are 63 km and 107 km, respectively. The assumed true measurement epoch coordinates of the fiducial stations were taken from their published values. Fig. 2 shows the location of fiducial stations and rover station. 2.2. GIPSY/OASIS processing strategy GIPSY/OASIS is developed by the NASA’s Jet Propulsion Laboratory (JPL). GIPSY/OASIS software applies single-receiver ambiguity resolution. The algorithm in GIPSY/OASIS processes dual-frequency GPS data from a single receiver together with wide-lane and phase bias estimates from the global network of GPS receivers that were used to generate the orbit and clock solutions for the GPS satellites (Bertiger et al., 2010). The algorithm performs double difference ambiguity resolution between the rover station and one of the stations in the network that
Table 1 GAMIT/GLOBK processing strategy. Elevation cut-off angle Weighting with elevation Epoch interval GNSS system Ephemerides Ionospheric effect Second order ionospheric effect Phase initial ambiguity Antex file Troposphere Troposphere gradients Code differential bias Reference frame realization Reference frame Solid Earth Tides
10 degree Applied 30 s GPS IGS precise ephemerides (Griffiths and Ray, 2015) Removed by L1, L2 linear combination Applied with using IONEX file Wide lane and narrow line combination IGS08.atx (Schmid et al. 2016) GPT2 model (Lagler et al. 2013) Computed Up to date DCB file (Wang et al. 2016) Generalized constraints with using GLOBK Igb08 (Griffiths and Ray, 2015) Applied (Watson et al., 2006)
Please cite this article as: S. Alcay, S. Ogutcu, I. Kalayci et al., Displacement monitoring performance of relative positioning and Precise Point Positioning (PPP) methods using simulation apparatus, Advances in Space Research, https://doi.org/10.1016/j.asr.2018.11.003
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Fig. 2. Location of the used stations.
were used to generate the orbit and clock solutions for the GPS satellites with using wide-lane and phase bias. For the details of the processing strategy of GIPSY/OASIS software, authors refer to Bertiger et al. (2010). Table 2 summarizes the processing parameters used in this study. 3. Significance testing of horizontal and vertical displacements Displacements were determined on the basis of comparing two epochs. Then null hypothesis and its alternative hypothesis were formed as follows ((7) and (8)); Table 2 GIPSY/OASIS processing strategy. Elevation cut-off angle Weighting with elevation Epoch interval GNSS system Ephemerides
Ionospheric effect Second order ionospheric effect Phase initial ambiguity Antex file Troposphere Troposphere gradients Code differential bias Reference frame Solid Earth Tides
10 degree Applied 30 s GPS FLINN precise ephemerides (JPL fiducial frame) (ftp://sideshow.jpl.nasa.gov/pub/ JPL_GPS_Products/Final/2018/) Removed by L1, L2 linear combination Applied with using IONEX file Wide lane and narrow line combination IGS08.atx (Schmid et al. 2016) GPT2 model (Lagler et al. 2013) Computed Up to date DCB file (Wang et al. 2016) Igb08 (Griffiths and Ray, 2015) Applied (Watson et al.,2006)
H 0 : EðdÞ ¼ 0 no displacement between two epochs
ð7Þ
H 0 : EðdÞ–0 displacement between two epochs
ð8Þ
Where 00 E00 represents ‘‘expected value”. The test statistic was computed as T Test ¼
d sim rmseðhorizontal=vertical=azimuth angleÞ
ð9Þ
and compared to the critical value ðT crit ) with a significance level of a. Where rms stands for root mean square error and computed using following Eq. (10), rffiffiffiffiffiffiffiffiffi ½VV ð10Þ RMSE ¼ n Where ‘‘v” stands for the differences between simulated (true) displacements and derived displacements. ‘‘n” is the number of obtained differences. In the test (9), it is possible to use standard deviation ‘‘r” instead of rms. Standard deviation values are calculated based on variancecovariance matrix and exhibits inner precision. However, the variance-covariance matrix derived from scientific software underestimates the magnitude of the error, mainly due to the fact that physical correlations are neglected (Kashani et al., 2004). The major goal of this study is to test the obtained results according to the true displacements. Therefore we used RMSE values which were computed based on true displacements. If T < T crit , the null hypothesis is accepted, otherwise (T > T crit Þ the null hypothesis is rejected. Details, regarding the critical value ðT crit ) including calculation procedure, formulations etc., authors refer to Savsˇek-Safic´ et al. (2006). As described in Savsˇek-Safic´ et al. (2006), the value of T crit is taken to be 3 as is used as a ‘‘rule of thumb”
Please cite this article as: S. Alcay, S. Ogutcu, I. Kalayci et al., Displacement monitoring performance of relative positioning and Precise Point Positioning (PPP) methods using simulation apparatus, Advances in Space Research, https://doi.org/10.1016/j.asr.2018.11.003
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which is larger than the value derived from distributed function of the test statistics. Therefore in this study, ‘‘3” was taken as critical value. 4. Results Computed displacements and azimuth angle between two consecutive epochs from each data set were assessed in terms of RMS error, minimum detectable displacement and azimuth angle. RMSEhorizontal
displacement
¼
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi X ffi horizontal displacement2residuals =n
ð11Þ
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r X ¼ vertical displacement2residuals =n
RMSEvertical
displacement
RMSEazimuth
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi X ¼ azimuth2residuals =n
ð12Þ
ð13Þ
Where, RMSEhorizontal displacement , RMSEvertical displacement and RMSEazimuth are the RMS errors of horizontal displacement, vertical displacement and azimuth angle, respectively. Outlier detection was applied using 3-sigma rule for displacements and azimuth angle (Lehmann, 2013; Klos et al., 2015). The results are given in the following subsections w.r.t. each method and data set. 4.1. Results of the processed data In this section, results of each data sets (24 h, 12 h, 8 h, 4 h, 2 h) including rms errors according to the formulas (11–13), outlier numbers, minimum detectable amount of displacement and azimuth angle according to the formula (9), minimum-maximum-mean values of residuals are given in the following tables. RMSE results based on 24 h observation illustrate that accuracy of the relative method is better than PPP method in horizontal-vertical directions and azimuth angle (Table 3). Residuals illustrate the differences between relative/PPP estimated displacements and simulated (true) displacements. Relative-estimated residuals range from 2.5 mm to 4.0 mm in the horizontal direction and
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7.3 mm to 9.9 mm in the vertical direction. PPP estimated residuals range between (4.6) mm – (5.7) mm and (11.1) mm – (11.6) mm in the horizontal and vertical directions, respectively. In addition, according to the test value (T Test ) and critical value ðT crit ), minimum detectable amount derived by relative method is 6.0 mm in the horizontal and 12.3 mm in the vertical directions. Minimum displacement detected by PPP method is 8.1 mm and 19.2 mm in horizontal and vertical directions, respectively. Moreover, in terms of minimum detectable azimuth angle based on relative method exhibits better results comparing to the PPP method. Besides Table 3, Fig. 3 illustrates the true displacements and relative-PPP estimated displacements for 24 h processing results. The other sessions are not given due to the size of the manuscript. Table 4 shows the results of relative and PPP methods based on 12 h observation. Horizontal and vertical results of both methods are close to the 24 h results. In terms of derived accuracy for horizontal-vertical displacements and azimuth angle, relative method produces better results comparing to the PPP. Minimum and maximum residuals of relative and PPP methods in horizontal direction range from 6.4 mm to 5.5 mm and -9.5 mm to 12.7 mm, respectively, whereas they reach in the order of cm level in vertical direction. In addition, RMSE of relative derived azimuth angle is approx. equal to the 24 h solutions. Minimum detected significant displacements by relative and PPP solutions are 7.2 mm and 13.8 mm in horizontal, 18.3 mm and 21.6 mm in vertical directions, respectively. Table 5 gives the details of both methods based on 8 h data processing. Accuracy of the relative-estimated horizontal displacements and azimuth angle are close to the 24 h and 12 h solutions. Nevertheless, RMSE of vertical displacement is a little larger (7.9 mm) comparing to the 24 h results. PPP-estimated RMSE values are close to the 24 and 12 h solutions in all components. It is possible to detect 8.4 mm and 13.8 mm horizontal displacements by relative and PPP methods, respectively. Minimum detectable amount of vertical displacement is 23.7 mm for relative method and 21.3 mm for PPP method. Table 6 shows statistical details of both methods based on 4 h results. While, RMSE values of relative and PPP methods in horizontal directions are 3.2 mm and 5.3 mm
Table 3 Statistical results of 24 h processing. RMSE
Outlier
Minimum detectable amount
Min residual
Max residual
Mean residual
Relative method Horizontal (mm) Vertical (mm) Azimuth angle (degree)
2.0 4.1 8.2
0 0 0
6.0 12.3 24.6
2.5 7.3 24
4.0 9.9 13
0.5 0.2 1.7
PPP method Horizontal (mm) Vertical (mm) Azimuth angle (degree)
2.7 6.4 13.4
0 0 1
8.1 19.2 40.2
4.6 11.1 41.4
5.7 11.6 48.5
0.6 0.5 2.0
Please cite this article as: S. Alcay, S. Ogutcu, I. Kalayci et al., Displacement monitoring performance of relative positioning and Precise Point Positioning (PPP) methods using simulation apparatus, Advances in Space Research, https://doi.org/10.1016/j.asr.2018.11.003
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Fig. 3. Displacement values of 24 h processing.
Table 4 Statistical results of 12 h processing. RMSE
Outlier
Minimum detectable amount
Min residual
Max residual
Mean residual
Relative method Horizontal (mm) Vertical (mm) Azimuth angle (degree)
2.4 6.1 7.9
0 0 1
7.2 18.3 23.7
6.4 10.5 23.3
5.5 16.3 19.2
0.6 2.3 1.1
PPP method Horizontal (mm) Vertical (mm) Azimuth angle (degree)
4.6 7.2 19.1
0 0 2
13.8 21.6 57.3
9.5 15.6 61.2
12.7 11.0 74.6
0.6 0.2 3.1
Table 5 Statistical results of 8 h processing. RMSE
Outlier
Minimum detectable amount
Min residual
Max residual
Mean residual
Relative method Horizontal (mm) Vertical (mm) Azimuth angle (degree)
2.8 7.9 9.5
0 1 2
8.4 23.7 28.5
4.4 11.2 32.9
6.4 25.6 19.2
1.1 3.5 2.1
PPP method Horizontal (mm) Vertical (mm) Azimuth angle (degree)
4.6 7.1 17.2
1 1 3
13.8 21.3 51.6
8.8 15.2 30.8
10.8 12.6 92.2
0.9 0.1 5.5
respectively, RMSE of vertical displacements is around 1 cm for both methods. Minimum significant horizontal displacement values detected by relative and PPP methods are 9.6 mm and 15.9 mm, respectively. However in the vertical direction minimum detectable amount is 30.0 mm for relative method and 30.6 mm for PPP method. In addition, the magnitude of minimum and maximum residuals are not exceed 10 mm and 15 mm in the horizontal direction,
33 mm and 28 mm in the vertical direction corresponding to relative and PPP methods, respectively. Associated with the maximum residuals of azimuth angle minimum detectable amount of PPP is worse than the relative derived azimuth angle. For 2 h processing, the outlier numbers and maximumminimum residuals are larger than that of the other data sets (Table 7). Minimum and maximum residuals are in
Please cite this article as: S. Alcay, S. Ogutcu, I. Kalayci et al., Displacement monitoring performance of relative positioning and Precise Point Positioning (PPP) methods using simulation apparatus, Advances in Space Research, https://doi.org/10.1016/j.asr.2018.11.003
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Table 6 Statistical results of 4 h processing. RMSE
Outlier
Minimum detectable amount
Min residual
Max residual
Mean residual
Relative method Horizontal (mm) Vertical (mm) Azimuth angle (degree)
3.2 10.0 15.1
1 2 2
9.6 30.0 45.3
7.5 17.3 50.1
9.9 32.2 47.7
1.0 3.5 2.7
PPP method Horizontal (mm) Vertical (mm) Azimuth angle (degree)
5.3 10.2 21.0
1 2 4
15.9 30.6 63.0
11.3 22.6 89.5
15.0 27.3 74.0
1.2 0.1 3.2
Table 7 Statistical results of 2 h processing. RMSE
Outlier
Minimum detectable amount
Min residual
Max residual
Mean residual
Relative method Horizontal (mm) Vertical (mm) Azimuth angle (degree)
4.2 14.1 23.9
8 4 8
12.6 42.3 71.7
12.9 45.1 71.7
19.1 50.8 88.6
1.3 3.6 1.5
PPP method Horizontal (mm) Vertical (mm) Azimuth angle (degree)
5.9 13.7 27.2
1 4 9
17.7 41.1 81.6
13.4 43.1 103.3
17.8 45.8 120.9
1.7 0.4 0.5
the order of cm level for horizontal-vertical directions. Minimum horizontal displacement detected by relative method and PPP solutions are 12.6 mm and 17.7 mm, respectively. However in the vertical direction minimum detectable amount is 42.3 mm for relative method and 41.1 mm for PPP. As it is shown from the Tables 3–7, mean residuals of vertical components corresponding to relative method are worse than the PPP method. This shows that systematic errors in vertical component of PPP are less than the relative method in this study. In order to investigate the possible reasons of outliers and high residuals for 2 h sessions, ambiguity resolution, ionospheric condition and meteorological events were examined. In order to see whether there is any ionospheric activity during the collection of GPS data, geomagnetic storm (kp), geomagnetic activity (Dst) and solar activity (F10.7) indices were examined. According to the indice values, no ionospheric storm was detected during the data collection period. However, it is observed that ambiguity resolution and wet tropospheric delay play a significant role. Low percentage of narrow lane ambiguity resolution
is the main reason of outliers and high residuals among the data sets. Some outliers and high residuals in horizontal and vertical components for 2 h sessions are induced by the meteorological events known as thunderstorm and heavy rain. Table 8 shows the derived outliers/residuals and ambiguity resolution for each method during the meteorological events. As given in Table 8, there are thunderstorms between 10 and 12 UT on DOY 179, 215 and heavy rain 18-20 UT on DOY 215. The largest outlier is observed as 22.1 cm in vertical direction on DOY 179, 10-12 UT based on relative method. In addition, ambiguity resolution is rather low for both methods. The main reason for low narrow-lane ambiguity resolution is due to the noise of the code data. Table 9 shows the statistics of ambiguity resolutions for 2 h non-outlier observations. Compared to the Table 8 and Table 9, it is seen that meteorological events mostly effect the ambiguity resolution. Fig. 4 depicts the positive (yellow) and negative residuals (green) of one-way (un-differenced) ionosphere-free linear phase combination for each satellite-station pair for
Table 8 Outliers related to meteorological events. Software
Time interval
Horizontal outliers/residuals (cm)
Vertical outliers (cm)
Ambiguity resolution
Meteorological event
Relative Method PPP Method Relative Method PPP Method Relative Method PPP Method
10–12 10–12 10–12 10–12 18–20 18–20
5.3 1.3 1.5 3.4 0.05 0.4
22.1 10.8 9.8 9.4 2.6 4.3
19% 53% 39% 28% 71% 42%
Thunderstorm Thunderstorm Thunderstorm Thunderstorm Heavy rain Heavy rain
(DOY:179) (DOY:179) (DOY:215) (DOY:215) (DOY:215) (DOY:215)
(Narrow-lane) (Wide-narrow lane) (Narrow-lane) (Wide-narrow lane) (Narrow-lane) (Wide-narrow lane)
Please cite this article as: S. Alcay, S. Ogutcu, I. Kalayci et al., Displacement monitoring performance of relative positioning and Precise Point Positioning (PPP) methods using simulation apparatus, Advances in Space Research, https://doi.org/10.1016/j.asr.2018.11.003
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Table 9 Statistics of ambiguity resolution.
4.2. Differences according to the accuracy thresholds
Statistics (relative method) Minimum Maximum Mean
Ambiguity resolution (narrow-lane) 57% 100% 89%
Statistics (PPP method) Minimum Maximum Mean
Ambiguity resolution (wide-narrow lane) 61% 90% 72%
Besides the maximum-minimum differences and RMSE values which are given in the previous subsection, a set of thresholds were specified in order to examine the percentage of the residuals according to their magnitudes. Tables 10 and 11 give the thresholds of the horizontal and vertical differences, respectively, according to observation times spanning long to short data lengths. From Table 10, it is apparent that the magnitude of data according to the thresholds for both methods improves as the observation time increases. Based on the longest (24 h) and shortest (2 h) observation periods, most of the horizontal residuals (50%) are between 1 and 3 mm for both methods. In terms of the number of magnitudes and their thresholds, relative method provides better results comparing to the PPP. Furthermore, even in the shortest time span (2 h), the differences did not exceed 13–20 mm threshold values by two methods. Table 11 depicts the thresholds of vertical differences based on relative and PPP methods. In terms of the magnitudes, vertical differences are higher than the horizontal differences. Although there is no residuals larger than 20 mm even for the 2 h results in horizontal direction, 4.2% and 5.1% of 2 h vertical residuals are larger than 30 mm based on relative and PPP methods, respectively. Similar to the horizontal values, the superiority of the relative method over PPP method are distinguished in terms of vertical values. In addition, it is possible to observe the influence of observation duration more clearly comparing to the horizontal results.
each measurement epoch after the adjustment. These residuals contain non-modelled error sources such as multipath, water vapor and higher-order ionospheric delay. Since higher-order ionospheric effect (up to second order) is modelled in both relative and PPP techniques, the remaining residuals mainly indicate the multipath, wet delay and phase noise. Positive residuals mean the observed phase is more delayed than the modelled phase, while negative residuals mean the observed phase is less delayed than modelled one after the adjustment. Since the phase multipath of the test station is theoretically constant, the relatively large amount of residuals in the sky plot for DOY 179 could be interpreted as the relatively large amount of wet delay compared to DOY 181. The plot was created using GAMIT/GLOBK software. As depicted in Fig. 5, the wet delay changes in DOY 179 10-12 UT are more fluctuated compared to DOY 181. This would be the main reason for the largest vertical outlier among the data sets.
Fig. 4. Positive and negative phase residuals for each arch of GPS satellites for DOY 179, 181 (10-12 UT), the red bar in the plots is scale (10 mm). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Please cite this article as: S. Alcay, S. Ogutcu, I. Kalayci et al., Displacement monitoring performance of relative positioning and Precise Point Positioning (PPP) methods using simulation apparatus, Advances in Space Research, https://doi.org/10.1016/j.asr.2018.11.003
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Fig. 5. Changes of wet zenith tropospheric delay for DOY 179, 181 (10-12 UT).
Table 10 Thresholds of horizontal differences. Threshold of Dif. (mm)
0–1
1–3
3–5
5–8
8–13
13–20
20–30
30-
Relative method (horizontal) 24 h (%) 12 h (%) 8 h (%) 4 h (%) 2 h (%)
40.0 32.5 20.0 27.7 23.7
50.0 52.5 51.7 42.9 34.1
10.0 10.0 23.3 14.3 22.4
5.0 5.0 13.4 14.7
1.7 4.3
0.9
PPP method (horizontal) 24 h (%) 12 h (%) 8 h (%) 4 h (%) 2 h (%)
20.0 10.0 8.5 11.8 13.0
50.0 30.0 32.2 23.5 28.0
25.0 37.5 33.9 30.3 19.7
5.0 17.5 18.6 22.7 21.8
5.0 6.8 9.2 15.1
2.5 2.5
Threshold of Dif. (mm)
0–1
1–3
3–5
5–8
8–13
Relative method (vertical) 24 h (%) 12 h (%) 8 h (%) 4 h (%) 2 h (%)
13–20
20–30
30-
25.0 12.5 8.5 11.9 5.5
40.0 35.0 25.4 12.7 14.8
10.0 15.0 20.3 16.1 11.0
20.0 20.0 22.0 16.1 20.3
5.0 12.5 10.2 22.0 18.2
5.0 11.9 18.6 13.6
1.7 1.7 12.3
0.8 4.2
PPP method (vertical) 24 h (%) 12 h (%) 8 h (%) 4 h (%) 2 h (%)
5.0 7.5 15.3 11.9 5.9
30.0 17.5 13.6 13.6 12.3
15.0 17.5 22.0 8.5 16.5
20.0 22.5 23.7 23.7 15.3
30.0 30.0 18.6 22.9 24.6
5.0 6.8 13.6 11.4
5.9 8.9
5.1
Table 11 Thresholds of vertical differences.
5. Conclusions This study was conducted to evaluate the displacement monitoring performance of relative and PPP methods in horizontal and vertical directions. Analysis based on
24 h, 12 h, 8 h observation durations for both methods reveals high consistency to determine true displacements in horizontal direction. However vertical displacement residuals are a little larger comparing to the horizontal results for all data sets (24 h-2 h). The superiority of the rel-
Please cite this article as: S. Alcay, S. Ogutcu, I. Kalayci et al., Displacement monitoring performance of relative positioning and Precise Point Positioning (PPP) methods using simulation apparatus, Advances in Space Research, https://doi.org/10.1016/j.asr.2018.11.003
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ative method over PPP is observed particularly in the horizontal direction. In terms of minimum detectable horizontal displacements, while relative method provides better than 1 cm even based on 4 h processing, PPP method requires long time span to reach similar amount of minimal detectable displacements (24 h). However, both methods cannot provide better than 1 cm in the vertical direction even using 24 h observation. In this study, direction of the deformation also computed using azimuth angle. It is observed that if the displacement between two points are large enough, direction of the deformation can be computed accurately. Since the used distance is too short for the determination of azimuth direction (25 cm), the obtained accuracy is relatively low. However, it is important to illustrate the superiority of the relative method over PPP for deformation direction. The significance of the experiment indicates that besides relative positioning method, PPP method can be used in many deformation monitoring applications including seismic event, landslide, structure etc., depending on the displacement monitoring performance. The authors recommend that in order to obtain reliable results during the displacement monitoring period and analysis, meteorological events and ambiguity resolution should be taken into consideration. Acknowledgements This study was funded by the Scientific Research Projects Grant of Necmettin Erbakan University (Project No: 161219013).The authors would like to express their gratitude to NASA Jet Propulsion Laboratory (JPL) and Massachusetts Institute of Technology (MIT) for providing GIPSY/OASIS and GAMIT/GLOBK scientific software. The authors would like to thank to Dr. Huseyin Zahit Selvi for designing Fig. 2 using GMT. The fourth author is awarded a grant by The Scientific and Technological Research Council of Turkey (TUBITAK) to perform a research on High-rate GNSS-PPP Method for GNSS seismology and Structural Health Monitoring Applications at School of Earth and Planetary Sciences, Curtin University, Australia. He would like to thank TUBITAK, Science fellowships and Grant Programs Department for the support. The authors also thank to the reviewers for their reviews, critical comments and helpful suggestions, which improved the manuscript greatly. References Bao, Y., Guo, W., Wang, G., Gan, W., Zhang, M., Shen, J., 2018. Millimeter-Accuracy structural deformation monitoring using standalone GPS: Case study in Beijing, China. J. Surv. Eng. 144 (1). https:// doi.org/10.1061/(ASCE)SU.1943-5428.0000242. Bertiger, W., Desai, S.D., Haines, B., Harvey, N., Moore, A.W., Owen, S., Weiss, J.P., 2010. Single receiver phase ambiguity resolution with GPS data. J. Geod. 84 (5), 327–337. Chatterjee, R.S., Thapa, S., Sıngh, K.B., Varunakumar, G., Raju, E.V.R., 2015. Detecting, mapping and monitoring of land subsidence in Jharia Coalfield, Jharkhand, India by spaceborne differential interferometric
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