Evaluation of the ability of the high-rate multi-GNSS PPP-AR method to detect dynamic behaviors in horizontal direction
Year 2022,
, 952 - 960, 14.10.2022
Mert Bezcioğlu
,
Cemal Özer Yiğit
,
Ahmet Anıl Dindar
,
Özgür Avcı
Abstract
This study investigates the ability of traditional-PPP (Precise Point Positioning) and PPP-AR (Ambiguity Resolution) techniques in structural health monitoring and Global Navigation Satellite Systems (GNSS)-seismology applications, and the contribution of multi-GNSS observations to both methods. To evaluate the performances of the methods, harmonic oscillations with amplitudes ranging from 5 mm to 10 mm and frequency between 0.3 Hz and 1.2 Hz, representing possible structural motions, were generated using a shake table. Furthermore, the 1989 Loma Prieta earthquake was simulated to examine the performance of PPP techniques in GNSS-seismology applications. The data collected at 20 Hz sampling rate were evaluated employing the traditional-PPP and PPP-AR techniques using only-Global Positioning System (GPS) and GPS/Galileo satellite observations, and the results were compared with Linear Variable Differential Transformer (LVDT) data in the frequency and time domain. Although the outcomes revealed that the frequency and amplitude values obtained from both methods with different satellite combinations in the frequency domain were comparable to each other, they clearly demonstrate that the superiority of the PPP-AR technique over the traditional-PPP technique in the time domain and the contribution of multi-GNSS observations.
References
- M. Celebi, GPS in pioneering dynamic monitoring of long-period structures, Soil Dynamics and Earthquake Engineering, 20(5-8), 477-483, 2000. https://doi.org/10.1016/S0267-7261(00)00094-4.
- X. Li, L. Ge, E. Ambikairajah, C. Rizos, Y. Tamura and A. Yoshida, Full-scale structural monitoring using an integrated GPS and accelerometer system, GPS Solution, 10(4), 233-247, 2006. https://doi.org/ 10.1007/s10291-006-0023-y.
- P. Breuer, T. Chmielewski, P. Gorski, E. Konopka and L. Tarczynski, The Stuttgart TV tower—Displacement of the top caused by the effects of sun and wind, Engineering Structures, 30(10), 2771-2781, 2008. https://doi.org/10.1016/j.engstruct.2008.03.008.
- H.S. Park, H.G. Sohn, I.S. Kim and J.H. Park, Application of GPS to monitoring of wind-induced responses of high-rise buildings, Structural Design of Tall and Special Buildings, 17(1), 117-132, 2008. https://doi.org/10.1002/tal.335.
- C.O. Yigit, X. Li, C. Inal, L. Ge and M. Yetkin, Preliminary evaluation of precise inclination sensor and GPS for monitoring full-scale dynamic response of a tall reinforced concrete building, Journal of Applied Geodesy, 4(2), 103-113, 2010. https://doi.org/10. 1515/jag.2010.010.
- P. Górski, Dynamic characteristic of tall industrial chimney estimated from GPS measurement and frequency domain decomposition, Engineering Structures, 148, 277-292, 2017. https://doi.org/ 10.1016/ j.engstruct.2017.06.066.
- G.W. Roberts, X. Meng and A. Dodson, Integrating a global positioning system and accelerometers to monitor deflection of bridges, Journal of Surveying Engineering, 130(2), 65-72, 2004. https://doi.org/ 10.1061/(ASCE)0733-9453(2004)130:2(65).
- X. Meng, A.H. Dodson and G.W. Roberts, Detecting bridge dynamics with GPS and triaxial accelerometers, Engineering Structures, 29(11), 3178-3184, 2007. https://doi.org/10.1016/j.engstruct.2007.03.012.
- F. Moschas and S. Stiros, Measurement of the dynamic displacements and of the modal frequencies of a short-span pedestrian bridge using GPS and an accelerometer, Engineering Structures, 33(1), 10-17, 2011. https://doi.org/10.1016/j.engstruct.2010.09.013.
- Y. Xu, J.M.W. Brownjohn, D. Hester and K.Y. Koo, Long-span bridges: Enhanced data fusion of GPS displacement and deck accelerations, Engineering Structures, 147, 639-651, 2017. https://doi.org/ 10.1016/j.engstruct.2017.06.018.
- W.S. Chan, Y.L. Xu, X.L. Ding, Y.L. Xiong and W.J. Dai, Assessment of dynamic measurement accuracy of GPS in three directions, Journal of Surveying Engineering, 132(3), 108-117, 2006. https://doi.org/ 10.1061/(ASCE)0733-9453(2006)132:3(108).
- A. Nickitopoulou, K. Protopsalti and S.C. Stiros, Monitoring dynamic and quasi-static deformations of large flexible engineering structures with GPS: Accuracy, limitations and promises, Engineering Structures, 28(10), 1471–1482, 2006. https://doi.org/ 10.1016/j.engstruct.2006.02.001.
- P.A. Psimoulis and S.C. Stiros, Experimental assessment of the accuracy of GPS and RTS for the determination of the parameters of oscillation of major structures, Computer-Aided Civil and Infrastructure Engineering, 23(5), 389-403, 2008. https://doi.org/ 10.1111/j.1467-8667.2008.00547.x.
- G. Wang, F. Blume, C. Meertens, P. Ibanez and M. Schulze, Performance of high-rate kinematic GPS during strong shaking: Observations from shake table tests and the 2010 Chile earthquake, Journal of Geodetic Science, 2(1), 1-15, 2011. https://doi.org/ 10.1186/BF03352300.
- P. Xu, C. Shi, R. Fang, J. Liu, X. Niu, Q. Zhang and T. Yanagidani, High-rate Precise Point Positioning (PPP) to measure seismic wave motions: an experimental comparison of GPS PPP with inertial measurement units, Journal of Geodesy, 87, 361-372, 2013. https://doi.org/10.1007/s00190-012-0606-z.
- J.F. Zumberge, M.B. Heflin, D.C. Jefferson, M.M. Watkins and F.H. Webb, Precise Point Positioning for the efficient and robust analysis of GPS data from large networks, Journal of Geophysical Research, 102(B3), 5005-5017, 1997. https://doi.org/10.1029/96JB03860.
- J. Kouba and P. Héroux, Precise Point Positioning using IGS orbit and clock products, GPS Solutions, 5, 12-28, 2001. https://doi.org/10.1007/PL00012883.
- T. Li, J. Wang and D. Laurichesse, Modeling and quality control for reliable Precise Point Positioning integer ambiguity resolution with GNSS modernization, GPS Solutions, 18(3), 429-442, 2014. https://doi.org/10.1007/s10291-013-0342-8.
- B. Karadeniz, M. Bezcioğlu, Ö.F. Bilgen ve C.Ö. Yiğit, GPS/Galileo PPP-AR ve PPP yöntemlerinin doğruluklarının gözlem süresi ve uydu kombinasyonları açısından incelenmesi, AKÜ FEMÜBİD, 21(6): 1377-1392, 2021. https://doi.org/ 10.35414/akufemubid.1003382.
- J.C. Savage, W. Gan, W.H. Prescott and J.L. Svarc, Strain accumulation across the coast ranges at the latitude of San Francisco 1994–2000, Journal of Geophysical Research, 109 (B3), B03413, 2004. https://doi.org/10.1029/2003JB002612.
- E. Calais, J.Y. Han, C. Demets and J.M. Nocquet, Deformation of the North American plate interior from a decade of continuous GPS measurements, Journal of Geophysical Research, 11(6), 1-23, 2006. https://doi.org/10.1029/2005JB004253
- J. Kouba, Measuring seismic waves induced by large earthquakes with GPS, Studia Geophysica et Geodaetica, 47, 741-755, 2003. https://doi.org/ 10.1023/A:1026390618355.
- A. Avallone, M. Marzario, A. Cirella, A. Piatanesi, A. Rovelli, C. Di Alessandro, E. D’Anastasio, N. D’Agostino, R. Giuliani and M. Mattone, Very high rate (10 Hz) GPS seismology for moderate-magnitude earthquakes: The case of the Mw 6.3 L’Aquila (central Italy) event, Journal of Geophysical Research: Solid Earth, 116(B2), B02305, 2011. https://doi.org/ 10.1029/2010JB007834.
- P. Xu, C. Shi, R. Fang, J. Liu, X. Niu, Q. Zhang and T. Yanagidani, High-rate Precise Point Positioning (PPP) to measure seismic wave motions: an experimental comparison of GPS PPP with inertial measurement units, Journal of Geodesy, 87, 361-372, 2013. https://doi.org/10.1007/s00190-012-0606-z.
- Z. Nie, R. Zhang, G. Liu, Z. Jia, D. Wang, Y. Zhou and M. Lin, GNSS seismometer: Seismic phase recognition of real-time high-rate GNSS deformation waves, Journal of Applied Geophysics, 135, 328-337, 2016. https://doi.org/10.1016/j.jappgeo.2016.10.026.
- J. Paziewski, R. Sieradzki and R. Baryla, Multi-GNSS high-rate RTK, PPP and novel direct phase observation processing method: Application to precise dynamic displacement detection, Measurement Science and Technology, 29(3), 035002, 2018. https://doi.org/10.1088/1361-6501/aa9ec2.
- P. Xu, Y. Shu, X. Niu, W. Yao and Q. Chen, High-rate multi-GNSS attitude determination: Experiments, comparisons with inertial measurement units and applications of GNSS rotational seismology to the 2011 Tohoku Mw9.0 earthquake, Measurement Science and Technology, 30(2), 024003, 2019. https://doi.org/ 10.1088/1361-6501/aaf987.
- F. Moschas, A. Avallone, V. Saltogianni and S.C. Stiros, Strong motion displacement waveforms using 10-Hz Precise Point Positioning GPS: an assessment based on free oscillation experiments, Earthquake Engineering Structural Dynamics, 43(12), 1853-1866, 2014. https://doi.org/10.1002/eqe.2426.
- M. Bezcioğlu, B. Karadeniz, C.Ö. Yiğit, A.A. Dindar, F. Bezir ve Ö. Avcı, Gerçek Zamanlı GNSS VADASE yaklaşımının dinamik deplasmanları yakalayabilme kabiliyetinin incelenmesi, Harita Dergisi, 167, 1-11, 2022
- X. Li, M. Ge, X. Zhang, Y. Zhang, B. Guo, R. Wang, J. Klotz and J. Wickert, Real-time high-rate co-seismic displacement from ambiguity-fixed precise point positioning: Application to earthquake early warning, Geophysical Research Letters, 40(2), 295-300, 2013. https://doi.org/10.1002/grl.50138.
- S. Choy, S. Bisnath, and C. Rizos, Uncovering common misconceptions in GNSS Precise Point Positioning and its future prospect. GPS Solutions, 21, 13-22, 2017. https://doi.org/10.1007/s10291-016-0545-x.
- P. Li, X. Zhang, and F. Guo, Ambiguity resolved precise point positioning with GPS and BeiDou. Journal of Geodesy, 91, 25-40, 2017. https://doi.org/10.1007/s00190-016-0935-4.
- X. Li, X. Li, Y. Yuan, K. Zhang, X. Zhang, and J. Wickert, 2018. Multi-GNSS phase delay estimation and PPP ambiguity resolution: GPS, BDS, GLONASS, Galileo. Journal of Geodesy, 92, 579-608, 2018. https://doi.org/10.1007/s00190-017-1081-3.
- J. Geng, J. Guo, X. Meng, and K. Gao, Speeding up PPP ambiguity resolution using triple-frequency GPS/BeiDou/Galileo/QZSS data, Journal of Geodesy, 94(6), 1-15, 2020. https://doi.org/10.1007/s00190-019-01330-1.
- G. Katsigianni, S. Loyer, and F. Perosanz, PPP and PPP-AR Kinematic Post-Processed Performance of GPS-Only, Galileo-Only and Multi-GNSS, Remote Sensing, 11, 2477, 2019. https://doi.org/ 10.3390/rs11212477.
- D. Psychas, S. Verhagen and P.J.G. Teunissen, Precision analysis of partial ambiguity resolution-enabled PPP using multi-GNSS and multi-frequency signals, Advances in Space Research, 66, 2075–2093, 2020. https://doi.org/10.1016/j.asr.2020.08.010.
- M. Bezcioglu, C.O. Yigit, and A. El-Mowafy, Kinematic PPP-AR in Antarctic: Comparing Methods for Precise Positioning, Sea Technology, 60(2), 20-23, 2019.
- M. Bezcioğlu, C.Ö. Yiğit ve M.N. Bodur, Kinematik PPP-AR ve Geleneksel PPP Yöntemlerin Performanslarının Değerlendirilmesi: Antarktika Yarımadası Örneği, AKÜ FEMÜBİD, 19(1), 162-169, 2019. https://doi.org/10.35414/akufemubid.467336.
- C.O. Yigit, A. El-Mowafy, A.A. Dindar, M. Bezcioglu and I. Tiryakioglu, Investigating performance of high-rate GNSS-PPP and PPP-AR for structural health monitoring: Dynamic tests on shake table, Journal of Surveying Engineering, 147(1), 05020011:1-14, 2021. https://doi.org/10.1061/(ASCE)SU.1943-5428.0000343.
- https://github.com/YizeZhang/Net_Diff, Accessed 05 July 2022.
- J. Geng, X. Chen, Y. Pan, S. Mao, C. Li, J. Zhou and K. Zhang, PRIDE PPP-AR: An Open-Source Software for GPS PPP Ambiguity Resolution, GPS Solutions, 23, 91, 2019. https://doi.org/10.1007/s10291-019-0888-1.
- O.F. Atiz, S. Ogutcu, S. Alcay, P. Li and I. Bugdayci, Performance investigation of LAMBDA and bootstrapping methods for PPP narrow-lane ambiguity resolution, Geo-Spatial Information Science, 24(4), 604-614, 2021.
https://doi.org/10.1080/10095020.2021.1942236.
Yüksek zamansal çözünürlüklü çoklu-GNSS PPP-AR yönteminin yatay yönlü dinamik davranışları tespit edebilme yeteneğinin değerlendirilmesi
Year 2022,
, 952 - 960, 14.10.2022
Mert Bezcioğlu
,
Cemal Özer Yiğit
,
Ahmet Anıl Dindar
,
Özgür Avcı
Abstract
Bu çalışma geleneksel-Hassas Nokta Konumlama (PPP: Precise Point Positioning) ve PPP-AR (Ambiguity Resolution) yöntemlerinin yapı sağlığı izlemeleri ve Global Navigation Satellite Systems (GNSS)-sismolojisi uygulamalarındaki etkinliğini ve ilgili tekniklere çoklu-GNSS gözlemlerinin katkısını araştırmaktadır. Yöntemlerin performanslarını değerlendirmek için yatay yönde hareket edebilme kabiliyetine sahip bir sarsma tablası kullanılarak olası yapısal hareketleri temsil eden 5 mm ila 10 mm arasında değişen genliklere ve 0.3 Hz ila 1.2 Hz arasında frekanslara sahip harmonik salınımlar üretilmiştir. Ayrıca, 1989 Loma Prieta depremi, PPP tekniklerinin GNSS-sismolojisi uygulamalarındaki performanslarını incelemek için simule edilmiştir. 20 Hz örneklem aralığında toplanan veriler sadece-Global Positioning System (GPS) ve GPS/Galileo uydu gözlemleri kullanılarak geleneksel-PPP ve PPP-AR teknikleri ile değerlendirilmiş, elde edilen sonuçlar frekans ve zaman alanında Linear Variable Differential Transformer (LVDT) verileri ile karşılaştırılmıştır. Sonuçlar frekans alanında farklı uydu kombinasyonları ile iki yöntemden de elde edilen frekans ve genlik değerlerinin benzer olduğunu ifade ederken, zaman alanında PPP-AR tekniğinin geleneksel-PPP tekniğine olan üstünlüğünü ve çoklu-GNSS gözlemlerinin katkısını açık bir şekilde ortaya koymaktadır.
References
- M. Celebi, GPS in pioneering dynamic monitoring of long-period structures, Soil Dynamics and Earthquake Engineering, 20(5-8), 477-483, 2000. https://doi.org/10.1016/S0267-7261(00)00094-4.
- X. Li, L. Ge, E. Ambikairajah, C. Rizos, Y. Tamura and A. Yoshida, Full-scale structural monitoring using an integrated GPS and accelerometer system, GPS Solution, 10(4), 233-247, 2006. https://doi.org/ 10.1007/s10291-006-0023-y.
- P. Breuer, T. Chmielewski, P. Gorski, E. Konopka and L. Tarczynski, The Stuttgart TV tower—Displacement of the top caused by the effects of sun and wind, Engineering Structures, 30(10), 2771-2781, 2008. https://doi.org/10.1016/j.engstruct.2008.03.008.
- H.S. Park, H.G. Sohn, I.S. Kim and J.H. Park, Application of GPS to monitoring of wind-induced responses of high-rise buildings, Structural Design of Tall and Special Buildings, 17(1), 117-132, 2008. https://doi.org/10.1002/tal.335.
- C.O. Yigit, X. Li, C. Inal, L. Ge and M. Yetkin, Preliminary evaluation of precise inclination sensor and GPS for monitoring full-scale dynamic response of a tall reinforced concrete building, Journal of Applied Geodesy, 4(2), 103-113, 2010. https://doi.org/10. 1515/jag.2010.010.
- P. Górski, Dynamic characteristic of tall industrial chimney estimated from GPS measurement and frequency domain decomposition, Engineering Structures, 148, 277-292, 2017. https://doi.org/ 10.1016/ j.engstruct.2017.06.066.
- G.W. Roberts, X. Meng and A. Dodson, Integrating a global positioning system and accelerometers to monitor deflection of bridges, Journal of Surveying Engineering, 130(2), 65-72, 2004. https://doi.org/ 10.1061/(ASCE)0733-9453(2004)130:2(65).
- X. Meng, A.H. Dodson and G.W. Roberts, Detecting bridge dynamics with GPS and triaxial accelerometers, Engineering Structures, 29(11), 3178-3184, 2007. https://doi.org/10.1016/j.engstruct.2007.03.012.
- F. Moschas and S. Stiros, Measurement of the dynamic displacements and of the modal frequencies of a short-span pedestrian bridge using GPS and an accelerometer, Engineering Structures, 33(1), 10-17, 2011. https://doi.org/10.1016/j.engstruct.2010.09.013.
- Y. Xu, J.M.W. Brownjohn, D. Hester and K.Y. Koo, Long-span bridges: Enhanced data fusion of GPS displacement and deck accelerations, Engineering Structures, 147, 639-651, 2017. https://doi.org/ 10.1016/j.engstruct.2017.06.018.
- W.S. Chan, Y.L. Xu, X.L. Ding, Y.L. Xiong and W.J. Dai, Assessment of dynamic measurement accuracy of GPS in three directions, Journal of Surveying Engineering, 132(3), 108-117, 2006. https://doi.org/ 10.1061/(ASCE)0733-9453(2006)132:3(108).
- A. Nickitopoulou, K. Protopsalti and S.C. Stiros, Monitoring dynamic and quasi-static deformations of large flexible engineering structures with GPS: Accuracy, limitations and promises, Engineering Structures, 28(10), 1471–1482, 2006. https://doi.org/ 10.1016/j.engstruct.2006.02.001.
- P.A. Psimoulis and S.C. Stiros, Experimental assessment of the accuracy of GPS and RTS for the determination of the parameters of oscillation of major structures, Computer-Aided Civil and Infrastructure Engineering, 23(5), 389-403, 2008. https://doi.org/ 10.1111/j.1467-8667.2008.00547.x.
- G. Wang, F. Blume, C. Meertens, P. Ibanez and M. Schulze, Performance of high-rate kinematic GPS during strong shaking: Observations from shake table tests and the 2010 Chile earthquake, Journal of Geodetic Science, 2(1), 1-15, 2011. https://doi.org/ 10.1186/BF03352300.
- P. Xu, C. Shi, R. Fang, J. Liu, X. Niu, Q. Zhang and T. Yanagidani, High-rate Precise Point Positioning (PPP) to measure seismic wave motions: an experimental comparison of GPS PPP with inertial measurement units, Journal of Geodesy, 87, 361-372, 2013. https://doi.org/10.1007/s00190-012-0606-z.
- J.F. Zumberge, M.B. Heflin, D.C. Jefferson, M.M. Watkins and F.H. Webb, Precise Point Positioning for the efficient and robust analysis of GPS data from large networks, Journal of Geophysical Research, 102(B3), 5005-5017, 1997. https://doi.org/10.1029/96JB03860.
- J. Kouba and P. Héroux, Precise Point Positioning using IGS orbit and clock products, GPS Solutions, 5, 12-28, 2001. https://doi.org/10.1007/PL00012883.
- T. Li, J. Wang and D. Laurichesse, Modeling and quality control for reliable Precise Point Positioning integer ambiguity resolution with GNSS modernization, GPS Solutions, 18(3), 429-442, 2014. https://doi.org/10.1007/s10291-013-0342-8.
- B. Karadeniz, M. Bezcioğlu, Ö.F. Bilgen ve C.Ö. Yiğit, GPS/Galileo PPP-AR ve PPP yöntemlerinin doğruluklarının gözlem süresi ve uydu kombinasyonları açısından incelenmesi, AKÜ FEMÜBİD, 21(6): 1377-1392, 2021. https://doi.org/ 10.35414/akufemubid.1003382.
- J.C. Savage, W. Gan, W.H. Prescott and J.L. Svarc, Strain accumulation across the coast ranges at the latitude of San Francisco 1994–2000, Journal of Geophysical Research, 109 (B3), B03413, 2004. https://doi.org/10.1029/2003JB002612.
- E. Calais, J.Y. Han, C. Demets and J.M. Nocquet, Deformation of the North American plate interior from a decade of continuous GPS measurements, Journal of Geophysical Research, 11(6), 1-23, 2006. https://doi.org/10.1029/2005JB004253
- J. Kouba, Measuring seismic waves induced by large earthquakes with GPS, Studia Geophysica et Geodaetica, 47, 741-755, 2003. https://doi.org/ 10.1023/A:1026390618355.
- A. Avallone, M. Marzario, A. Cirella, A. Piatanesi, A. Rovelli, C. Di Alessandro, E. D’Anastasio, N. D’Agostino, R. Giuliani and M. Mattone, Very high rate (10 Hz) GPS seismology for moderate-magnitude earthquakes: The case of the Mw 6.3 L’Aquila (central Italy) event, Journal of Geophysical Research: Solid Earth, 116(B2), B02305, 2011. https://doi.org/ 10.1029/2010JB007834.
- P. Xu, C. Shi, R. Fang, J. Liu, X. Niu, Q. Zhang and T. Yanagidani, High-rate Precise Point Positioning (PPP) to measure seismic wave motions: an experimental comparison of GPS PPP with inertial measurement units, Journal of Geodesy, 87, 361-372, 2013. https://doi.org/10.1007/s00190-012-0606-z.
- Z. Nie, R. Zhang, G. Liu, Z. Jia, D. Wang, Y. Zhou and M. Lin, GNSS seismometer: Seismic phase recognition of real-time high-rate GNSS deformation waves, Journal of Applied Geophysics, 135, 328-337, 2016. https://doi.org/10.1016/j.jappgeo.2016.10.026.
- J. Paziewski, R. Sieradzki and R. Baryla, Multi-GNSS high-rate RTK, PPP and novel direct phase observation processing method: Application to precise dynamic displacement detection, Measurement Science and Technology, 29(3), 035002, 2018. https://doi.org/10.1088/1361-6501/aa9ec2.
- P. Xu, Y. Shu, X. Niu, W. Yao and Q. Chen, High-rate multi-GNSS attitude determination: Experiments, comparisons with inertial measurement units and applications of GNSS rotational seismology to the 2011 Tohoku Mw9.0 earthquake, Measurement Science and Technology, 30(2), 024003, 2019. https://doi.org/ 10.1088/1361-6501/aaf987.
- F. Moschas, A. Avallone, V. Saltogianni and S.C. Stiros, Strong motion displacement waveforms using 10-Hz Precise Point Positioning GPS: an assessment based on free oscillation experiments, Earthquake Engineering Structural Dynamics, 43(12), 1853-1866, 2014. https://doi.org/10.1002/eqe.2426.
- M. Bezcioğlu, B. Karadeniz, C.Ö. Yiğit, A.A. Dindar, F. Bezir ve Ö. Avcı, Gerçek Zamanlı GNSS VADASE yaklaşımının dinamik deplasmanları yakalayabilme kabiliyetinin incelenmesi, Harita Dergisi, 167, 1-11, 2022
- X. Li, M. Ge, X. Zhang, Y. Zhang, B. Guo, R. Wang, J. Klotz and J. Wickert, Real-time high-rate co-seismic displacement from ambiguity-fixed precise point positioning: Application to earthquake early warning, Geophysical Research Letters, 40(2), 295-300, 2013. https://doi.org/10.1002/grl.50138.
- S. Choy, S. Bisnath, and C. Rizos, Uncovering common misconceptions in GNSS Precise Point Positioning and its future prospect. GPS Solutions, 21, 13-22, 2017. https://doi.org/10.1007/s10291-016-0545-x.
- P. Li, X. Zhang, and F. Guo, Ambiguity resolved precise point positioning with GPS and BeiDou. Journal of Geodesy, 91, 25-40, 2017. https://doi.org/10.1007/s00190-016-0935-4.
- X. Li, X. Li, Y. Yuan, K. Zhang, X. Zhang, and J. Wickert, 2018. Multi-GNSS phase delay estimation and PPP ambiguity resolution: GPS, BDS, GLONASS, Galileo. Journal of Geodesy, 92, 579-608, 2018. https://doi.org/10.1007/s00190-017-1081-3.
- J. Geng, J. Guo, X. Meng, and K. Gao, Speeding up PPP ambiguity resolution using triple-frequency GPS/BeiDou/Galileo/QZSS data, Journal of Geodesy, 94(6), 1-15, 2020. https://doi.org/10.1007/s00190-019-01330-1.
- G. Katsigianni, S. Loyer, and F. Perosanz, PPP and PPP-AR Kinematic Post-Processed Performance of GPS-Only, Galileo-Only and Multi-GNSS, Remote Sensing, 11, 2477, 2019. https://doi.org/ 10.3390/rs11212477.
- D. Psychas, S. Verhagen and P.J.G. Teunissen, Precision analysis of partial ambiguity resolution-enabled PPP using multi-GNSS and multi-frequency signals, Advances in Space Research, 66, 2075–2093, 2020. https://doi.org/10.1016/j.asr.2020.08.010.
- M. Bezcioglu, C.O. Yigit, and A. El-Mowafy, Kinematic PPP-AR in Antarctic: Comparing Methods for Precise Positioning, Sea Technology, 60(2), 20-23, 2019.
- M. Bezcioğlu, C.Ö. Yiğit ve M.N. Bodur, Kinematik PPP-AR ve Geleneksel PPP Yöntemlerin Performanslarının Değerlendirilmesi: Antarktika Yarımadası Örneği, AKÜ FEMÜBİD, 19(1), 162-169, 2019. https://doi.org/10.35414/akufemubid.467336.
- C.O. Yigit, A. El-Mowafy, A.A. Dindar, M. Bezcioglu and I. Tiryakioglu, Investigating performance of high-rate GNSS-PPP and PPP-AR for structural health monitoring: Dynamic tests on shake table, Journal of Surveying Engineering, 147(1), 05020011:1-14, 2021. https://doi.org/10.1061/(ASCE)SU.1943-5428.0000343.
- https://github.com/YizeZhang/Net_Diff, Accessed 05 July 2022.
- J. Geng, X. Chen, Y. Pan, S. Mao, C. Li, J. Zhou and K. Zhang, PRIDE PPP-AR: An Open-Source Software for GPS PPP Ambiguity Resolution, GPS Solutions, 23, 91, 2019. https://doi.org/10.1007/s10291-019-0888-1.
- O.F. Atiz, S. Ogutcu, S. Alcay, P. Li and I. Bugdayci, Performance investigation of LAMBDA and bootstrapping methods for PPP narrow-lane ambiguity resolution, Geo-Spatial Information Science, 24(4), 604-614, 2021.
https://doi.org/10.1080/10095020.2021.1942236.