{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:59:09Z","timestamp":1760241549662,"version":"build-2065373602"},"reference-count":51,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2018,5,15]],"date-time":"2018-05-15T00:00:00Z","timestamp":1526342400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Precise orbit determination solutions for the two spacecrafts TerraSAR-X (TSX) and TanDEM-X (TDX) are operationally computed at the German Space Operations Center (GSOC\/DLR). This publication makes use of 6 years of TSX and TDX orbit solutions for a detailed orbit validation. The validation compares the standard orbit products with newly determined enhanced orbit solutions, which additionally consider GPS ambiguity fixing and utilize a macro model for modeling non-gravitational forces. The technique of satellite laser ranging (SLR) serves as a key measure for validating the derived orbit solutions. In addition, the synthetic aperture radar (SAR) instruments on-board both spacecrafts are for the first time employed for orbit validation. Both the microwave instrument and the optical laser approach are compared and assessed. The average SLR residuals, obtained from the TSX and TDX enhanced orbit solutions within the analysis period, are at 1.6 \u00b1 11.4 mm ( 1 \u03c3 ) and 1.2 \u00b1 12.5 mm, respectively. Compared to the standard orbit products, this is an improvement of 33 % in standard deviation. The corresponding radar range biases are in the same order and amount to \u2212 3.5 \u00b1 12.5 mm and 4.5 \u00b1 14.9 mm. Along with the millimeter level position offsets in radial, along-track and cross-track inferred from the SLR data on a monthly basis, the results confirm the advantage of the enhanced orbit solutions over the standard orbit products.<\/jats:p>","DOI":"10.3390\/rs10050762","type":"journal-article","created":{"date-parts":[[2018,5,15]],"date-time":"2018-05-15T11:36:13Z","timestamp":1526384173000},"page":"762","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["Long-Term Validation of TerraSAR-X and TanDEM-X Orbit Solutions with Laser and Radar Measurements"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8014-7146","authenticated-orcid":false,"given":"Stefan","family":"Hackel","sequence":"first","affiliation":[{"name":"German Space Operations Center, Deutsches Zentrum f\u00fcr Luft- und Raumfahrt, 82230 Wessling, Germany"}]},{"given":"Christoph","family":"Gisinger","sequence":"additional","affiliation":[{"name":"Remote Sensing Technology Institute, Deutsches Zentrum f\u00fcr Luft- und Raumfahrt, 82230 Wessling, Germany"}]},{"given":"Ulrich","family":"Balss","sequence":"additional","affiliation":[{"name":"Remote Sensing Technology Institute, Deutsches Zentrum f\u00fcr Luft- und Raumfahrt, 82230 Wessling, Germany"}]},{"given":"Martin","family":"Wermuth","sequence":"additional","affiliation":[{"name":"German Space Operations Center, Deutsches Zentrum f\u00fcr Luft- und Raumfahrt, 82230 Wessling, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4783-745X","authenticated-orcid":false,"given":"Oliver","family":"Montenbruck","sequence":"additional","affiliation":[{"name":"German Space Operations Center, Deutsches Zentrum f\u00fcr Luft- und Raumfahrt, 82230 Wessling, Germany"}]}],"member":"1968","published-online":{"date-parts":[[2018,5,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"606","DOI":"10.1109\/TGRS.2009.2031062","article-title":"The TerraSAR-X Mission and System Design","volume":"48","author":"Werninghaus","year":"2010","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_2","first-page":"1000","article-title":"TanDEM-X: A TerraSAR-X Add-On Satellite for Single-Pass SAR Interferometry","volume":"2","author":"Moreira","year":"2004","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"661","DOI":"10.1109\/TGRS.2010.2060264","article-title":"Imaging geodesy\u2014Toward centimeter-level ranging accuracy with TerraSAR-X","volume":"49","author":"Eineder","year":"2011","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1007\/s00190-011-0515-6","article-title":"Mitigation of atmospheric perturbations and solid Earth movements in a TerraSAR-X time-series","volume":"86","author":"Schubert","year":"2012","journal-title":"J. Geod."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1782","DOI":"10.1109\/TGRS.2014.2348859","article-title":"Precise Three-Dimensional Stereo Localization of Corner Reflectors and Persistent Scatterers with TerraSAR-X","volume":"53","author":"Gisinger","year":"2015","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Balss, U., Gisinger, C., and Eineder, M. (2018). Measurements on the Absolute 2-D and 3-D Localization Accuracy of TerraSAR-X. Remote Sens., 10.","DOI":"10.3390\/rs10040656"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"3317","DOI":"10.1109\/TGRS.2007.900693","article-title":"TanDEM-X: A Satellite Formation for High-Resolution SAR Interferometry","volume":"45","author":"Krieger","year":"2007","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1859","DOI":"10.1109\/TGRS.2008.2006983","article-title":"TerraSAR-X Precise Trajectory Estimation and Quality Assessment","volume":"47","author":"Yoon","year":"2009","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1007\/BF02285050","article-title":"Satellite laser ranging and its applications","volume":"37","author":"Tapley","year":"1985","journal-title":"Celest. Mech."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Arnold, D., Montenbruck, O., Hackel, S., and So\u015bnica, K. (2018). Satellite Laser Ranging to Low Earth Orbiters\u2014Orbit and Network Validation. J. Geod., 1\u201320.","DOI":"10.1007\/s00190-018-1140-4"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Balss, U., Cong, X., Brcic, R., Rexer, M., Minet, C., Breit, H., Eineder, M., and Fritz, T. (2012, January 22\u201327). High precision measurement on the absolute localization accuracy of TerraSAR-X. Proceedings of the 2012 IEEE International Geoscience and Remote Sensing Symposium (IGARSS), Munich, Germany.","DOI":"10.1109\/IGARSS.2012.6351217"},{"key":"ref_12","unstructured":"Kahle, R., Kazeminejad, B., Kirschner, M., Yoon, Y., Kiehling, R., and D\u2019Amico, S. (2007, January 24\u201328). First In-Orbit Experience of TerraSAR-X flight dynamic operations. Proceedings of the 20th International Symposium on Space Flight Dynamics, Annapolis, MD, USA."},{"key":"ref_13","unstructured":"Buckreuss, S., Balzer, W., M\u00fchlbauer, P., Werninghaus, R., and Pitz, W. (2003, January 21\u201325). The TerraSAR-X satellite project. Proceedings of the 2003 IEEE International Geoscience and Remote Sensing Symposium, Toulouse, France."},{"key":"ref_14","unstructured":"Eineder, M., Runge, H., Boerner, E., Bamler, R., Adam, N., Sch\u00e4ttler, B., Breit, H., and Suchandt, S. (2000, January 1\u20135). SAR interferometry with TerraSAR-X. Proceedings of the FRINGE 2003 Workshop, Frascati, Italy."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1007\/s10291-003-0055-5","article-title":"In-flight performance analysis of the CHAMP BlackJack GPS Receiver","volume":"7","author":"Montenbruck","year":"2003","journal-title":"GPS Solut."},{"key":"ref_16","unstructured":"Montenbruck, O., Yoon, Y., Ardaens, J.S., and Ulrich, D. (2008, January 2\u20135). In-Flight Performance Assessment of the Single Frequency MosaicGNSS Receiver for Satellite Navigation. Proceedings of the 7th International ESA Conference on Guidance, Navigation and Control Systems, County Kerry, Ireland."},{"key":"ref_17","unstructured":"Wermuth, M., Montenbruck, O., and van Helleputte, T. (2010, January 3\u20136). GPS High Precision Orbit Determination Tools (GHOST). Proceedings of the 4th International Conference on Astrodynamics Tools and Techniques, Madrid, Spain."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"547","DOI":"10.1007\/s00190-016-0982-x","article-title":"Model improvements and validation of TerraSAR-X precise orbit determination","volume":"91","author":"Hackel","year":"2017","journal-title":"J. Geod."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Montenbruck, O., Hackel, S., and J\u00e4ggi, A. (2017). Precise orbit determination of the Sentinel-3A altimetry satellite using ambiguity-fixed GPS carrier phase observations. J. Geod.","DOI":"10.1007\/s00190-017-1090-2"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"991","DOI":"10.1007\/s00190-012-0559-2","article-title":"Zero-difference GPS ambiguity resolution at CNES-CLS IGS Analysis Center","volume":"86","author":"Loyer","year":"2012","journal-title":"J. Geod."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1007\/s00190-015-0876-3","article-title":"Absolute IGS antenna phase center model igs08.atx: status and potential improvements","volume":"90","author":"Schmid","year":"2016","journal-title":"J. Geod."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"6109","DOI":"10.1002\/2016JB013098","article-title":"ITRF2014: A new release of the International Terrestrial Reference Frame modeling nonlinear station motions","volume":"121","author":"Altamimi","year":"2016","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1007\/BF03655303","article-title":"Effects of antenna orientation on GPS carrier phase","volume":"18","author":"Wu","year":"1993","journal-title":"Manuscr. Geod."},{"key":"ref_24","unstructured":"Mayer-G\u00fcrr, T., Pail, R., Schuh, W.D., Kusche, J., Baur, O., and J\u00e4ggi, A. (2012, January 9\u201312). The new combined satellite only model GOCO03s. Proceedings of the International Symposium on Gravity, Geoid and Height Systems GGHS2012, Venice, Italy."},{"key":"ref_25","unstructured":"Eanes, R.J., and Bettadpur, S. (1995). The CSR 3.0 Global Ocean Tide Model: Diurnal and Semi-Diurnal Ocean Tides from TOPEX\/POSEIDON Altimetry, Center for Space Research, University of Texas at Austin. Technical Report 6."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1175\/2010JTECHA1521.1","article-title":"Radiometric Performance of the CERES Earth Radiation Budget Climate Record Sensors on the EOS Aqua and Terra Spacecraft through April 2007","volume":"28","author":"Priestley","year":"2011","journal-title":"J. Atmos. Ocean. Technol."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1468","DOI":"10.1029\/2002JA009430","article-title":"NRLMSISE-00 empirical model of the atmosphere: Statistical comparisons and scientific issues","volume":"107","author":"Picone","year":"2002","journal-title":"J. Geophys. Res."},{"key":"ref_28","unstructured":"Shampine, L.F., and Gordon, M.K. (1975). Computer Solution of Ordinary Differential Equations: The Initial Value Problem, W.H. Freeman & Co., Ltd."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1016\/S0273-1177(02)00277-6","article-title":"The International Laser Ranging Service","volume":"30","author":"Pearlman","year":"2002","journal-title":"Adv. Space Res."},{"key":"ref_30","unstructured":"Neubert, R., Grunwaldt, L., and Neubert, J. (1998, January 21\u201325). The Retro-Reflector for the CHAMP Satellite: Final Design and Realization. Proceedings of the 11th International Workshop on Laser Ranging, Deggendorf, Germany."},{"key":"ref_31","unstructured":"International Laser Ranging Service (2017, June 08). SLRF2014 Station Coordinates, Available online: ftp:\/\/ftp.cddis.eosdis.nasa.gov\/pub\/slr\/products\/resource\/SLRF2014_POS+VEL_2030.0_170605.snx."},{"key":"ref_32","unstructured":"Ray, R. (1999). A Global Ocean Tide Model from TOPEX\/Poseidon Altimeter: GOT99."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"L14602","DOI":"10.1029\/2004GL020308","article-title":"High-accuracy zenith delay prediction at optical wavelengths","volume":"31","author":"Mendes","year":"2004","journal-title":"Geophys. Res. Lett."},{"key":"ref_34","unstructured":"Pavlis, E. (2009, January 19). SLRF2008: The ILRS reference frame for SLR POD contributed to ITRF2008. Proceedings of the 2009 Ocean Surface Topography Science Team Meeting, Buellton, CA, USA."},{"key":"ref_35","unstructured":"International Association of Geodesy (2017, December 25). International Laser Ranging Service Mission Priorities as of December 25, 2017, Available online: https:\/\/ilrs.cddis.eosdis.nasa.gov\/missions\/mission_operations\/priorities\/index.htmll."},{"key":"ref_36","unstructured":"International Laser Ranging Service (2015, January 15). TerraSAR-X, Available online: http:\/\/ilrs.gsfc.nasa.gov\/missions\/satellite_missions\/current_missions\/tsar_general.html."},{"key":"ref_37","unstructured":"Cumming, I.G., and Wong, F.H. (2005). Digital Processing of Synthetic Aperture Radar Data, Artech House."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"727","DOI":"10.1109\/TGRS.2009.2035497","article-title":"TerraSAR-X SAR Processing and Products","volume":"48","author":"Breit","year":"2010","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_39","unstructured":"(2018, March 26). TerraSAR-X Ground Segment Basic Product Specification Document. TX-GS-DD-3302, v1.9, 09.10.2014. Available online: http:\/\/sss.terrasar-x.dlr.de."},{"key":"ref_40","unstructured":"D\u00f6ring, B., and Schwerdt, M.R.B. (2007, January 4\u20135). TerraSAR-X Calibration Ground Equipment. Proceedings of the Wave Propagation in Communication, Microwaves Systems and Navigation (WFMN), Chemnitz, Germany."},{"key":"ref_41","unstructured":"Petit, G., and Luzum, B. (2010). IERS Conventions (2010), Verlag des Bundesamts f\u00fcr Kartographie und Geod\u00e4sie. Available online: http:\/\/tai.bipm.org\/iers\/conv2010\/conv2010.html."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"588","DOI":"10.1109\/TASSP.1981.1163621","article-title":"Algorithms for Ambiguity Function Processing","volume":"ASSP-29","author":"Stein","year":"1981","journal-title":"IEEE Trans. Acoust. Speech Signal Process."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1109\/LGRS.2004.843203","article-title":"Accuracy of Differential Shift Estimation by Correlation and Split-Bandwidth Interferometry for Wideband and Delta-k SAR Systems","volume":"2","author":"Bamler","year":"2005","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Balss, U., Breit, H., Fritz, T., Steinbrecher, U., Gisinger, C., and Eineder, M. (2014, January 13\u201318). Analysis of Internal Timings and Clock Rates of TerraSAR-X. Proceedings of the 2014 IEEE International Geoscience and Remote Sensing Symposium (IGARSS), Quebec City, QC, Canada.","DOI":"10.1109\/IGARSS.2014.6947024"},{"key":"ref_45","unstructured":"Byram, S., Hackman, C., and Tracey, J. (2011, January 20\u201323). Computation of a High-Precision GPS-Based Troposphere Product by the USNO. Proceedings of the 24th international technical meeting of the satellite division of the institute of navigation (ION GNSS 2011), Portland, OR, USA."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1007\/s00190-011-0444-4","article-title":"ITRF2008: An improved solution of the international terrestrial reference frame","volume":"85","author":"Altamimi","year":"2011","journal-title":"J. Geod."},{"key":"ref_47","unstructured":"Richter, B., Dick, W.R., and Schwegmann, W. (2003, January 23\u201324). Local Ties between the Reference Points at the Fundamentalstation Wettzell. Proceedings of the IERS Workshop on Site Co-Location, Matera, Italy. Available online: https:\/\/www.iers.org\/IERS\/EN\/Publications\/publications.html."},{"key":"ref_48","unstructured":"Kl\u00fcgel, T., M\u00e4hler, S., and Schade, C. (2011, January 16\u201320). Ground Survey and Local Ties at the Geodetic Observatory Wettzell. Proceedings of the 17th International Workshop on Laser Ranging, Bad Koetzting, Germany. Available online: https:\/\/cddis.nasa.gov\/lw17\/."},{"key":"ref_49","unstructured":"International Earth Rotation and Reference Systems Service (IERS) (2018, March 26). The International Terrestrial Reference Frame (ITRF). Available online: https:\/\/www.iers.org\/IERS\/EN\/DataProducts\/ITRF\/itrf.html."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"677","DOI":"10.1109\/TGRS.2009.2035308","article-title":"Final TerraSAR-X Calibration Results Based on Novel Efficient Methods","volume":"48","author":"Schwerdt","year":"2010","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"879","DOI":"10.1016\/j.asr.2017.05.034","article-title":"Sentinel-1A\u2014First precise orbit determination results","volume":"60","author":"Peter","year":"2017","journal-title":"Adv. Space Res."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/10\/5\/762\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:04:23Z","timestamp":1760195063000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/10\/5\/762"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,5,15]]},"references-count":51,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2018,5]]}},"alternative-id":["rs10050762"],"URL":"https:\/\/doi.org\/10.3390\/rs10050762","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2018,5,15]]}}}