Almanya Münih Bölgesinde QDaedalus sistemi ile gözlemlenen astrojeodezik çekül sapma verilerinin GGMplus ve EGM2008 ile kestirilen değerlerle karşılaştırılması

Yıl 2020, Cilt: 41 Sayı: 3, 220 - 246, 15.12.2020

Müge ALBAYRAK Emel ZERAY ÖZTÜRK İbrahim Öztuğ BİLDİRİCİ Christian HİRT Sébastien GUİLLAUME Ck SHUM

https://doi.org/10.17824/yerbilimleri.740141

Öz

Astrojeodezik sistemlerle gözlemlenen astrojeodezik çekül sapma verisi, yeryuvarının gravite alanı ile ilgili önemli bilgiler sağlaması nedeniyle, yerbilimleri alanında, özellikle jeodezi ve jeofizik gibi bilimsel disiplinlerde, yersel, hava ve uydu gravite verilerinin kontrolü ve validasyonunda sıklıkla kullanılmaktadır. Bu çalışmada, Münih bölgesinde yer alan 10 nirengi noktasında astrojeodezik çekül sapma verisi gözlemleyebilmek için total station temelli QDaedalus sisteminden yararlanılmıştır. Gözlemlenen verilerin doğruluğunun ~0.2 yaysaniyesi (″) olduğu saptanmıştır. Yüksek doğruluklu bu veri seti, iki global gravite alan modelinin—Global Gravite Modeli plus (GGMplus) ve Yer Gravite Modeli 2008 (Earth Gravitational Model 2008–EGM2008)—kalitesini değerlendirebilmek için kullanılmıştır. QDaedalus sistemi ile gözlemlenen ve GGMplus modeli ile kestirilen çekül sapma bileşenleri arasındaki farklar, hem Kuzey-Güney (K-G) hem de Doğu-Batı (D-B) bileşenlerinde yaklaşık 0.2″ olmakla beraber, maksimum farklar K-G ve D-B bileşenlerinde sırasıyla ~0.3″ ve ~0.4″ olarak tespit edilmiştir. Sonuçlar EGM2008 modeli için analiz edildiğinde ise, gözlemlenen ve EGM2008 ile kestirilen çekül sapma bileşenleri arasındaki maksimum farkların K-G bileşeninde 0.9″; D-B bileşeninde ise 1.8″ olduğu saptanmıştır. Dolayısıyla, EGM2008 ile kestirilen değerlerin, GGMplus ile kestirilen değerlere göre doğruluğunun daha düşük olduğu görülmüştür. Bu çalışmadan elde edilen sonuçlar, daha önce İstanbul’da QDaedalus gözlemleri ile EGM2008 ve GGMplus modellerinin kıyaslandığı uygulama sonuçlarıyla da karşılaştırılmıştır. Bu makale kapsamında, İstanbul ve Münih’te aynı sistem ve global gravite alan modelleri kullanılarak elde edilen çekül sapma verileri arasındaki farkların sebepleri tartışılarak, GGMplus ile kestirilen çekül sapma veri setinin, hem Münih hem de İstanbul’da daha yüksek doğruluğa sahip olmasının nedenleri açıklanmıştır.

Anahtar Kelimeler

Astrojeodezik çekül sapması, astrojeodezik gözlemler, EGM2008, Global gravite alan modelleri, GGMplus, QDaedalus

Comparison of Observed Astrogeodetic Vertical Deflection Data Using QDaedalus System with the GGMplus- and EGM2008-predicted values in the Munich Region, Germany

Öz

Astrogeodetic vertical deflection (VD) data observed by astrogeodetic systems, which provide important information about Earth’s gravity field, are frequently used in the Earth Science disciplines, including geodesy and geophysics, to control and validate terrestrial, airborne and satellite gravity data. In this study, the total station-based QDaedalus system was used to observe astrogeodetic VD data at 10 benchmarks in the Munich region. The accuracy of these data is ~0.2 arcseconds (″). This high accuracy dataset was used to assess the quality of two global gravity field models—Global Gravitation Model Plus (GGMplus) and Earth Gravitational Model 2008 (EGM2008). The differences between the observed by QDaedalus and GGMplus-predicted VD data were ~0.2″ for both the North-South (N-S) and East-West (E-W) VD components, and reached a maximum of ~0.3″ and ~0.4″ for the N-S and E-W components, respectively. However, the maximum differences between the observed and EGM2008-predicted VD data for the N-S and E-W directions were 0.9″ and 1.8″, respectively. Thus, we found that the EGM2008-predicted values are less accurate than the predicted GGMplus values. The results of this study were compared with the results from a prior QDaedalus, and EGM2008 and GGMplus comparison study in Istanbul. In this article, we discuss the differences between the VD data obtained using the same QDaedalus system and global gravity field models in Istanbul and Munich, and explain the reasons for the higher accuracy of the VD data set predicted by GGMplus in both Munich and Istanbul.

Anahtar Kelimeler

Astrogeodetic observations, Astrogeodetic vertical deflections, EGM2008, GGMplus, Global gravity field models, QDaedalus

Kaynakça

• Abele, M., Balodis, J., Janpaule, I., Lasmane, I., Rubans, A., Zariņš, A., 2012. Digital zenith camera for vertical deflection determination. Geodesy and Cartography, 38(4),123–129. https://doi.org/10.3846/20296991.2012.755324.
• Albayrak M., Hirt C., 2018a. Determining the Astrogeodetic Geoid Profile of the Munich Region Using the QDaedalus System. Final Report BIDEB 2214-A, The Scientific and Technological Research Council of Turkey (TUBITAK), Ankara, Turkey, p. 63.
• Albayrak, M., Hirt, C., 2018b. Astrogeodetic observations at Geodetic Observatory Wettzell, Geodetic Observatory Wettzell, Technical Report, p.43.
• Albayrak, M., Hirt, C., Guillaume, S., Hauk, M., Halicioglu, K., 2018. Testing the QDaedalus measurement system for astrogeodetic observation of the gravity field. AGU Fall Meeting 2018, Abstracts. http://adsabs.harvard.edu/abs/2018AGUFM.G51F0534A.
• Albayrak, M., Halicioglu, K., Özlüdemir, MT., Basoglu, B., Deniz, R., Tyler, A.R.B., Aref, M.M., 2019a. The use of the automated digital zenith camera system in Istanbul for the determination of astrogeodetic vertical deflection. Boletim de Ciências Geodésicas 25(4).
• Albayrak, M., Hirt, C., Guillaume, S., Özlüdemir, M.T., Halicioglu, K., Basoglu, B., 2019b. New astrogeodetic observations of vertical deflections at the Istanbul astrogeodetic network demonstrate issues in global gravity models along coastlines. In 27th IUGG General Assembly.
• Albayrak, M., 2020. Assessment of global gravity models in coastal zones: A case study using astrogeodetic vertical deflections in Istanbul, Doktora Tezi, İstanbul Teknik Üniversitesi, Istanbul, Türkiye.
• Albayrak, M., Hirt, C., Guillaume, S., Halicioglu, K., Özlüdemir, M.T., Shum, C.K., 2020a. Quality assessment of global gravity field models in coastal zones: a case study using astrogeodetic vertical deflections in Istanbul, Turkey. Studia Geophysica et Geodaetica 64 (3). https://doi.org/10.1007/s11200-019-0591-2.
• Albayrak, M., Özlüdemir, M.T., Aref, M.M., Halicioglu, K., 2020b. Determination of Istanbul geoid using GNSS/levelling and valley cross levelling data. Geodesy and Geodynamics 11 (3). https://doi.org/10.1016/j.geog.2020.01.003.
• Albayrak, M., Guillaume, S., 2021. Astrojeodezide QDaedalus sistemi uygulamaları: Bir İnceleme (applications of the QDaedalus system in astrogeodesy: A Review), Harita Dergisi 165 (Baskıda).
• Andersen, O.B., Knudsen, P., 2009. DNSC08 mean sea surface and mean dynamic topography models. Journal of Geophysical Research: Oceans 114(C11). https://doi.org/10.1029/2008JC005179.
• Andersen, O.B., Knudsen, P., Berry, P.A., 2010. The DNSC08GRA global marine gravity field from double retracked satellite altimetry. Journal of Geodesy 84(3):191-9. https://doi.org/10.1007/s00190-009-0355-9.
• Ayan, T., Deniz, R., 2000. Fiziksel Jeodezi Ders Notu. İstanbul Teknik Üniversitesi, İnşaat Fakültesi, Jeodezi ve Fotogrametri Mühendisliği Bölümü, Jeodezi Anabilim Dalı, İstanbul, Türkiye.
• Ayan, T., Deniz, R., Arslan, E., Celik, R.N,. Denli, H.H., Akyılmaz, O., Ozsamlı, C., Özlüdemir, M.T., Erol, S., Erol, B., Acar, M., Mercan, H., & Tekdal, E., (2006). İstanbul GPS nirengi ağı (İGNA) 2005-2006 yenileme ölçü ve değerlendirmesi. Istanbul Teknik Üniversitesi Rapor 2005 /3123, Vol. 1, Istanbul, Turkey, s.186.
• Aydın, C., 2014. Fiziksel Jeodezi Ders Notu. Yıldız Teknik Üniversitesi, İnşaat Fakültesi, Harita Mühendisliği, İstanbul, Türkiye.
• Barnes, D., Factor, J.K., Holmes, S.A., Ingalls, S., Presicci, M.R., Beale, J., Fecher, T., 2015. Earth gravitational model 2020. AGU Fall Meeting 2015, Abstacts. https://ui.adsabs.harvard.edu/abs/2015AGUFM.G34A..03B/abstract.
• Bevis, M., Melini, D., Spada, G., 2016. On computing the geoelastic response to a disk load. Geophysical Journal International 205(3):1804-12. https://doi.org/10.1093/gji/ggw115.
• Bucha, B., Janák, J.A., 2013. MATLAB-based graphical user interface program for computing functionals of the geopotential up to ultra-high degrees and orders. Computers and Geosciences 56:186-96.
• Bürki, B., Müller, A., Kahle, H.G., 2004. DIADEM: The new digital astronomical deflection measuring system for high-precision measurements of deflections of the vertical at ETH Zurich. In: Marti U et al. (ed) Electronic proceedings of IAG GGSM2004 meeting in Porto, Portugal. Published also in CHGeoid2003, Report 03-33 A, Bundesamt für Landestopographie (swisstopo), Wabern, Schweiz.
• Bürki, B., Guillaume, S., Sorber, P., Oesch, H.P., 2010. DAEDALUS: A versatile usable digital clip-on measuring system for total stations. In 2010 International Conference on Indoor Positioning and Indoor Navigation. IEEE. https://doi.org/10.1109/IPIN.2010.5646270.
• Charalampous, E., Psimoulis, P., Guillaume, S., Spiridonakos, M., Klis, R., Bürki, B., Rothacher, M., Chatzi, E., Luchsinger, R., Feltrin, G., 2015. Measuring sub-mm structural displacements using QDaedalus: A digital clip-on measuring system developed for total stations. Applied Geomatics 7(2):91-101. https://doi.org/10.1007/s12518-014-0150-z.
• Featherstone, W.E., Rüeger, J.M., 2000. The importance of using deviations of the vertical in the reduction of terrestrial survey data to a geocentric datum. Trans-Tasman Surv 1(3):46–61. https://doi.org/10.1080/00050326.2000.10440341. [Erratum in The Australian Surveyor 47(1):7] https://doi.org/10.1080/00050356.2002.10558836.
• Förste, C., Bruinsma, S.L., Abrikosov, O., Lemoine, J.M., Marty, J.C., Flechtner, F., Balmino, G., Barthelmes, F., Biancale, R., 2014. EIGEN-6C4 The latest combined global gravity field model including GOCE data up to degree and order 2190 of GFZ Potsdam and GRGS Toulouse. GFZ Data Services, http://doi.org/10.5880/icgem.2015.1.
• Gilardoni, M., Reguzzoni, M., Sampietro, D., 2016. GECO: a global gravity model by locally combining GOCE data and EGM2008. Stud Geophys Geod 60, 228–247. https://doi.org/10.1007/s11200-015-1114-4.
• Guillaume, S., Bürki, B., Griffet, S., Durand, H.M., 2012. QDaedalus: Augmentation of total stations by CCD sensor for automated contactless high-precision metrology. In FIG working Week.
• Guillaume, S., 2015. Determination of a precise gravity field for the CLIC feasibility studies. PhD Thesis, Dissertation Nr. 22590, Eidgenössische Technische Hochschule ETH Zurich, Switzerland. https://doi.org/10.3929/ethz-a-010549038.
• Guillaume, S., Clerc, J., Bürki, B., 2015. QDaedalus digital clip-on measuring system for total station user manual, Institute of Geodesy and Photogrammetry, Geodesy and Geodynamics Laboratory, ETH Zurich, Switzerland.
• Guillaume, S., Clerc, J., Leyder, C., Ray, J., Kistler, M. 2016. Contribution of the image-assisted theodolite system QDaedalus to geodetic static and dynamic deformation monitoring. In 3rd Joint International Symposium on Deformation Monitoring(JISDM). http://www.fig.net/resources/proceedings/2016/2016_03_jisdm_pdf/nonreviewed/JISDM_2016_submission_66.pdf.
• Halicioglu, K., Deniz, R., Özener, H., 2016. Digital astro-geodetic camera system for the measurement of the deflections of the vertical: Tests and results. International Journal of Digital Earth 9(9):914–23. https://doi.org/10.1080/17538947.2016.1189612.
• Hauk, M., Hirt, C., Ackermann, C., 2017. Experiences with the QDaedalus system for astrogeodetic determination of deflections of the vertical. Survey Review 49(355):294-301. https://doi.org/10.1080/00396265.2016.1171960.
• Heiskanen, W.A., Moritz, H., 1967. Fiziksel Jeodezi (Çeviri:Onur GÜRKAN), W.H. Freeman and Co., San Francisco.
• Heiskanen, W.A., Moritz, H., 1984. Physical Geodesy. Institute of Physical Geodesy, Technical University Graz, Austria.
• Hirt, C., 2001. Automatic determination of vertical deflections in real-time by combining GPS and digital Zenith Camera for solving the "GPS-Height-Problem". In 14th International Technical Meeting of The Satellite Division of the Institute of Navigation 2001 (pp. 2540-51).
• Hirt, C., Bürki, B., 2003. The digital zenith camera-a new high-precision and economic astrogeodetic observation system for real-time measurement of deflections of the vertical. In 3rd Meeting International Gravity and Geoid Commission of the International Association of Geodesy (pp. 161-6). Editions Ziti. https://espace.curtin.edu.au/handle/20.500.11937/15374.
• Hirt, C., 2004. Entwicklung und Erprobung eines digitalen Zenitkamerasystems für die hochpräzise Lotabweichungsbestimmung. PhD Thesis, Wissen. Arb. Fach. Vermessungswesen Univ. Hannover Nr. 253 [Almanca]. http://edok01.tib.uni-hannover.de/edoks/e01dh04/393223965.pdf.
• Hirt, C., 2006. Monitoring and analysis of anomalous refraction using a digital zenith camera system. Astronomy & Astrophysics 459(1):283-90. https://doi.org/10.1051/0004-6361:20065485.
• Hirt, C., Bürki, B., 2006. Status of geodetic astronomy at the beginning of the 21st century. In: Festschrift Univ.- Prof. Dr.- Ing. Prof. h.c. Günter Seeber anlässlich seines 65, Geburtstages und der Verabschiedung in den Ruhestand, (Hirt C., Ed.), Wissenschaftliche Arbeiten der Fachrichtung Geodäsie und Geoinformatik an der Universität Hannover 258: 81–99.
• Hirt, C., Flury, J., 2008. Astronomical–topographic levelling using high-precision astrogeodetic vertical deflections and digital terrain model data. Journal of Geodesy 82(4–5):231–48. https://doi.org/10.1007/s00190-007-0173-x.
• Hirt, C., Seeber, G., 2008. Accuracy analysis of vertical deflection data observed with the Hannover Digital Zenith Camera System TZK2-D. Journal of Geodesy 82(6):347-56. https://doi.org/10.1007/s00190-007-0184-7.
• Hirt, C., 2010. Prediction of vertical deflections from high-degree spherical harmonic synthesis and residual terrain model data. Journal of Geodesy 84(3): 179–90. https://doi.org/10.1007/s00190-009-0354-x.
• Hirt, C., Bürki, B., Somieski, A., Seeber, G., 2010a. Modern determination of vertical deflections using digital zenith cameras. Journal of Surveying Engineering 136 (1): 1–12. https://ascelibrary.org/doi/pdf/10.1061/%28ASCE%29SU.1943-5428.0000009.
• Hirt, C., Marti, U., Bürki, B., Featherstone, W.E., 2010b. Assessment of EGM2008 in Europe using accurate astrogeodetic vertical deflections and omission error estimates from SRTM/DTM2006. 0 residual terrain model data. Journal of Geophysical Research: Solid Earth 115(B10).
• Hirt, C., Guillaume, S., Wisbar, A., Bürki, B., Sternberg, H., 2010c. Monitoring of the refraction coefficient in the lower atmosphere using a controlled setup of simultaneous reciprocal vertical angle measurements. Journal of Geophysical Research: Atmospheres 115(D21). https://doi.org/10.1029/2010JD014067.
• Hirt, C., Schmitz, M., Feldmann-Westendorff, U., Wübbena, G., Jahn, C.H., Seeber, G., 2011. Mutual validation of GNSS height measurements and high-precision geometric-astronomical leveling. GPS Solutions 15(2):149-59.
• Hirt, C., 2012. Anomalous atmospheric refraction and comments on 'fast and accurate determination of astronomical coordinates…' (Balodimos et al., 2003. Survey Review, 37(290): 269–75). Survey Review 44(327):285-9. https://doi.org/10.1179/175227012X13455477714906.
• Hirt, C., Claessens, S., Fecher, T., Kuhn, M., Pail, R., Rexer, M., 2013. New ultrahigh‐resolution picture of Earth's gravity field. Geophysical research letters 40(16):4279-83.
• Hirt, C., Wildermann, E., 2018. Reactivation of the Venezuelan vertical deflection data set from classical astrogeodetic observations. Journal of South American Earth Sciences 85: 97-107. https://doi.org/10.1016/j.jsames.2018.05.003.
• Ince, E.S., Barthelmes, F., Reißland, S., Elger, K., Förste, C., Flechtner, F., Schuh, H., 2019. ICGEM–15 years of successful collection and distribution of global gravitational models, associated services, and future plans. Earth System Science Data 11(2).
• Jekeli, C., 1999. An analysis of vertical deflections derived from high-degree spherical harmonic models. Journal of Geodesy 73(1): 10–22.
• Jekeli, C., 2012. Omission error, data requirements, and the fractal dimension of the geoid. InVII Hotine-Marussi Symposium on Mathematical Geodesy (pp. 181–187). Springer, Berlin, Heidelberg.
• Liang, W., Xu, X., Li, J., Zhu, G., 2018. The determination of an ultra-high gravity field model SGG-UGM-1 by combining EGM2008 gravity anomaly and GOCE observation data, Acta Geodaetica et Cartographica Sinica, 47 (4): 425–434, https://doi.org/10.11947/j.AGCS.2018.20170269.
• Morozova, K., Jäger, R., Balodis, J., Silabriedis, G., Kaminskis, J., Kalinka, M., Balodis, K., Mitrofanovs, I., 2019. Preliminary Results on Quasi-Geoid for Western Part of Latvia Using Digital-Zenith Camera and DFHRS V. 4.3 Software. Geophysica. 54(1):61-8.
• OpenStreetMap, 2019. OpenStreetMap Wiki (http://wiki.openstreetmap.org/wiki/Main_Page).
• Pail, R., Fecher, T., Barnes, D., Factor, J.F., Holmes, S.A., Gruber, T., Zingerle, P., 2018. Short note: the experimental geopotential model XGM2016. Journal of geodesy, 92(4), pp.443-451. https://doi.org/10.1007/s00190-017-1070-6.
• Pavlis, N.K., Holmes, S.A., Kenyon, S.C., Factor, J.K., 2012. The development and evaluation of the Earth Gravitational Model 2008 (EGM2008). Journal of geophysical research: solid earth 117(B4). https://doi.org/10.1029/2011JB008916.
• Pavlis, N.K., Holmes, S.A., Kenyon, S.C., Factor, J.K., 2013. Correction to “The development and evaluation of the Earth Gravitational Model 2008 (EGM2008)” Journal of Geophysical Research: Solid Earth 118(5):26-33. https://doi.org/10.1002/jgrb.50167.
• Pick, M., Picha, J., Vyskočil, V., 1973. Theory of earth's gravity field. Amsterdam, London, New York: Elsevier Scientific Publishing Company.
• Schack, P., Hirt, C., Hauk, M., Featherstone, W.E., Lyon, T.J., Guillaume, S., 2018. A high-precision digital astrogeodetic traverse in an area of steep geoid gradients close to the coast of Perth, Western Australia. Journal of Geodesy 92(10): 1143-1153. https://doi.org/10.1007/s00190-017-1107-x.
• Seeber, G., 2003. Satellite Geodesy. W. de Gruyter: Berlin, New York. Second edition.
• Sigl, R., 1991. Geodätische Astronomie. Wichmann, 4. Auflage.
• Smith, D.A., Holmes, S.A., Li, X., Guillaume, S., Wang, Y.M., Bürki, B., Roman, D.R., Damiani, T.M., 2013. Confirming regional 1 cm differential geoid accuracy from airborne gravimetry: the geoid slope validation survey of 2011. Journal of Geodesy 87(10–12):885–907. https://doi.org/10.1007/s00190-013-0653-0.
• Soler, T., Han, J.Y., Weston, N.D., 2013. On deflection of the vertical components and their transformations. Journal of Surveying Engineering 140(2):04014005(1-15). https://doi.org/10.1061/(ASCE)SU.1943-5428.0000126.
• Somieski, A.E., 2008. Astrogeodetic geoid and isostatic considerations in the North Aegean Sea, Greece (Doctoral dissertation, ETH Zurich). https://doi.org/10.3929/ethz-a-005710420.
• Tian, L., Guo, J., Han, Y., Lu, X., Liu, W., Wang, Z., Wang, B., Yin, Z., Wang, H., 2014. Digital zenith telescope prototype of China. Chinese Science Bulletin 59(17):1978-83. https://doi.org/10.1007/s11434-014-0256-z.
• Torge, W., Müller, J., 2012. Geodesy. 4th edition. De Gruyter, Berlin.
• Tóth, G., Völgyesi, L., 2017. Data processing of QDaedalus measurements. Geosciences and Engineering 5(8):147-64.
• Tóth, G., Völgyesi, L., 2018. Experiences of QDaedalus measurements. Geosciences and Engineering 6(9):75-86 u-blox AG, 2015. NEO-6T/LEA-6T product summary.
• Üstün, A., 2006. Fiziksel Jeodezi, Lisans Ders Notları. Selçuk Üniversitesi Jeodezi ve Fotogrametri Mühendisliği, Konya, Türkiye.
• Vittuari, L., Tini, M.A., Sarti, P., Serantoni, E., Borghi, A., Negusini, M., Guillaume, S., 2016. A comparative study of the applied methods for estimating deflection of the vertical in terrestrial geodetic measurements. Sensors 16(4):565. https://doi.org/10.3390/s16040565.
• Voigt, C., 2013. Astrogeodatische lotabweichungen zur validierung von schwerefeldmodellen, Doctoral Dissertation, Hannover: Fachrichtung Geodäsie und Geoinformatik der Leibniz University [Almanca].
• Volařík, T., Machotka, R., Kuruc, M., Puchrik, L., Jurčík, J., 2013. Determination of quasigeoid in local network using modern astrogeodetic technologies. Acta Geodynamica et Geomaterialia 10(172):437-42.
• Wang, B., Tian, L., Wang, Z., Yin, Z., Liu, W., Qiao, Q., Wang, H., Han, Y., 2014. Image and data processing of digital zenith telescope (DZT-1) of China. Chinese Science Bulletin 59(17):1984-91. https://doi.org/10.1007/s11434-014-0277-7.
• Wang, Y.M., Becker, C., Mader, G., Martin, D., Li, X., Jiang, T., Breidenbach, S., Geoghegan, C., Winester, D., Guillaume, S., Bürki, B., 2017. The Geoid slope validation survey 2014 and GRAV-D airborne gravity enhanced geoid comparison results in Iowa. Journal of Geodesy 91(10):1261-76. https://doi.org/10.1007/s00190-017-1022-1.
• Wielen, R., Schwan, H., Dettbarn, C., Lenhardt, H., Jahreiss, H., Jährling, R., 1999. Sixth Catalogue of Fundamental Stars (FK6). Part I. Basic fundamental stars with direct solutions. Veroeffentlichungen des Astronomischen Rechen-Instituts Heidelberg, Germany.
• Willi, D., Guillaume, S., 2019. Calibration of a Six-Axis Robot for GNSS Antenna Phase Center Estimation. Journal of Surveying Engineering. 145(4):04019016. https://doi.org/10.1061/(ASCE)SU.1943-5428.0000291.
• Zariņš, A., Rubans, A., Silabriedis, G., 2016. Digital zenith camera of the University of Latvia. Geodesy and Cartography 42(4):129-35. http://dx.doi.org/10.3846/20296991.2016.1268434.
• Zariņš, A., Rubans, A., Silabriedis, G., 2018. Performance analysis of Latvian zenith camera. Geodesy and Cartography 44(1):1-5. https://doi.org/10.3846/gac.2018.876.