{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:39:40Z","timestamp":1760150380497,"version":"build-2065373602"},"reference-count":37,"publisher":"MDPI AG","issue":"22","license":[{"start":{"date-parts":[[2023,11,10]],"date-time":"2023-11-10T00:00:00Z","timestamp":1699574400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62001216","61991422","SAST2017-78","NJ20220002","KYCX22_1318"],"award-info":[{"award-number":["62001216","61991422","SAST2017-78","NJ20220002","KYCX22_1318"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Shanghai Academy of Space-flight Technology Research","award":["62001216","61991422","SAST2017-78","NJ20220002","KYCX22_1318"],"award-info":[{"award-number":["62001216","61991422","SAST2017-78","NJ20220002","KYCX22_1318"]}]},{"name":"Key Laboratory of Radar Imaging and Microwave Photonics","award":["62001216","61991422","SAST2017-78","NJ20220002","KYCX22_1318"],"award-info":[{"award-number":["62001216","61991422","SAST2017-78","NJ20220002","KYCX22_1318"]}]},{"name":"Postgraduate Research &amp; Practice Innovation Program of Jiangsu Province","award":["62001216","61991422","SAST2017-78","NJ20220002","KYCX22_1318"],"award-info":[{"award-number":["62001216","61991422","SAST2017-78","NJ20220002","KYCX22_1318"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>A number of advanced SAR missions have been planned to launch, which can operate in fully polarimetric SAR interferometry mode to acquire structural parameters of global forests. Before the PolInSAR mission, the system configuration of vertical wavenumber kz must be carefully designed because it has a significant impact on the inversion performance. To minimize the estimation error of forest height caused by the system error from the future PolInSAR campaigns, it is valuable for us to optimize the vertical wavenumber. To quantitatively investigate the impact of kz on PolInSAR inversion performance, this paper proposes the optimization of kz based on the Cram\u00e9r\u2013Rao Lower Bound (CRLB) analysis. Extensive numerical CRLB simulations have been conducted to analyze the impact of several parameters, including extinction level, incident angle, and system decorrelation, etc., on the optimum kz. Finally, by minimizing the simulated CRLB, the numerical optimum kz maps are provided for the system engineers to easily design the system parameters.<\/jats:p>","DOI":"10.3390\/rs15225321","type":"journal-article","created":{"date-parts":[[2023,11,13]],"date-time":"2023-11-13T02:46:47Z","timestamp":1699843607000},"page":"5321","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Optimization of the Vertical Wavenumber for PolInSAR Inversion Performance Based on Numerical CRLB Analysis"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9999-3334","authenticated-orcid":false,"given":"Xiao","family":"Wang","sequence":"first","affiliation":[{"name":"College of Computer and Information Engineering, Nanjing Tech University, Nanjing 211816, China"}]},{"given":"Hong","family":"Li","sequence":"additional","affiliation":[{"name":"College of Computer and Information Engineering, Nanjing Tech University, Nanjing 211816, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,11,10]]},"reference":[{"key":"ref_1","unstructured":"Moreira, A., Hajnsek, I., Krieger, G., Papathanassiou, K., and Eineder, M. (2009, January 26\u201330). Tandem-L: Monitoring the Earth\u2019s Dynamics with InSAR and Pol-InSAR. Proceedings of the 4th International Workshop on Science and Applications of SAR Polarimetry and Polarimetric Interferometry (PolInSAR 2009), Frascati, Italy."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Krieger, G., Hajnsek, I., Papathanassiou, K.P., Eineder, M., Younis, M., Zan, F.D., Lopezdekker, P., Huber, S., Werner, M., and Prats, P. (2010, January 4\u20138). Tandem-L: A Mission for Monitoring Earth System Dynamics with High Resolution SAR Interferometry. Proceedings of the European Conference on Synthetic Aperture Radar, Pasadena, CA, USA.","DOI":"10.1109\/RADAR.2009.4977077"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2850","DOI":"10.1016\/j.rse.2011.03.020","article-title":"The BIOMASS mission: Mapping global forest biomass to better understand the terrestrial carbon cycle","volume":"115","author":"Quegan","year":"2011","journal-title":"Remote Sens. Environ."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Quegan, S., Chave, J., Dall, J., Toan, T.L., and Williams, M. (2012, January 22\u201327). The science and measurement concepts underlying the BIOMASS mission. Proceedings of the IEEE Geoscience and Remote Sensing Symposium, Munich, Germany.","DOI":"10.1109\/IGARSS.2012.6352350"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"294","DOI":"10.1109\/TGRS.2019.2936255","article-title":"Focusing the L-Band Spaceborne Bistatic SAR Mission Data Using a Modified RD Algorithm","volume":"58","author":"Li","year":"2019","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1735","DOI":"10.1109\/TGRS.2019.2948219","article-title":"An Advanced Phase Synchronization Scheme for LT-1","volume":"58","author":"Jin","year":"2020","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1551","DOI":"10.1109\/36.718859","article-title":"Polarimetric SAR Interferometry","volume":"36","author":"Cloude","year":"1998","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2352","DOI":"10.1109\/36.964971","article-title":"Single-baseline polarimetric SAR interferometry","volume":"39","author":"Papathanassiou","year":"2001","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1449","DOI":"10.1029\/96RS01763","article-title":"Vegetation characteristics and underlying topography from interferometric radar","volume":"31","author":"Treuhaft","year":"1996","journal-title":"Radio Sci."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1029\/1999RS900108","article-title":"Vertical structure of vegetated land surfaces from interferometric and polarimetric radar","volume":"35","author":"Treuhaft","year":"2000","journal-title":"Radio Sci."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Cloude, S.R. (2009). Polarisation: Applications in Remote Sensing, OUP Oxford.","DOI":"10.1093\/acprof:oso\/9780199569731.001.0001"},{"key":"ref_12","unstructured":"Lee, J.S., and Pottier, E. (2009). Polarimetric Radar Imaging: From Basics to Applications, CRC Press."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"481","DOI":"10.1109\/TGRS.2008.2009437","article-title":"Tropical-Forest-Parameter Estimation by Means of Pol-InSAR: The INDREX-II Campaign","volume":"47","author":"Hajnsek","year":"2009","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"5669","DOI":"10.1109\/TGRS.2019.2901531","article-title":"A PolinSAR Inversion Error Model on Polarimetric System Parameters for Forest Height Mapping","volume":"57","author":"Wang","year":"2019","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1109\/MGRS.2019.2954756","article-title":"Polarimetric SAR Interferometry: A Tutorial for Analyzing System Parameters","volume":"8","author":"Xue","year":"2020","journal-title":"IEEE Geosci. Remote Sens. Mag."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"R1","DOI":"10.1088\/0266-5611\/14\/4\/001","article-title":"Synthetic aperture radar interferometry","volume":"14","author":"Bamler","year":"1998","journal-title":"Inverse Probl."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1109\/5.838084","article-title":"Synthetic aperture radar interferometry","volume":"88","author":"Rosen","year":"2000","journal-title":"Proc. IEEE"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"4993","DOI":"10.1029\/JB091iB05p04993","article-title":"Topographic mapping from interferometric synthetic aperture radar","volume":"91","author":"Zebker","year":"1986","journal-title":"J. Geophys. Res."},{"key":"ref_19","unstructured":"Lee, S.K., Kugler, F., Hajnsek, I., and Papathanassiou, K. (2011, January 24\u201328). Multibaseline polarimetric SAR interferometry forest height inversion approaches. Proceedings of the 5th ESA POLinSAR Workshop, Frascati, Italy."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"3340","DOI":"10.1109\/TGRS.2010.2046669","article-title":"Estimation of the Backscatter Vertical Profile of a Pine Forest Using Single Baseline P-Band (Pol-)InSAR Data","volume":"48","author":"Garestier","year":"2010","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1528","DOI":"10.1109\/TGRS.2009.2032538","article-title":"Forest modelling for height inversion using single-baseline InSAR\/Pol-InSAR data","volume":"48","author":"Garestier","year":"2010","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Kangas, A., and Maltamo, M. (2006). Forest Inventory: Methodology and Application, Springer.","DOI":"10.1007\/1-4020-4381-3"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"3272","DOI":"10.1155\/ASP.2005.3272","article-title":"Spaceborne Polarimetric SAR Interferometry: Performance Analysis and Mission Concepts","volume":"2005","author":"Krieger","year":"2005","journal-title":"EURASIP J. Adv. Signal Process."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"S393","DOI":"10.1088\/0959-7174\/14\/2\/015","article-title":"Target detection beneath foliage using polarimetric synthetic aperture radar interferometry","volume":"14","author":"Cloude","year":"2004","journal-title":"Waves Random Media"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"5294","DOI":"10.1109\/TGRS.2015.2420996","article-title":"Forest Height Estimation by Means of Pol-InSAR Data Inversion: The Role of the Vertical Wavenumber","volume":"53","author":"Kugler","year":"2015","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1115","DOI":"10.1109\/LGRS.2011.2157891","article-title":"Cramer-Rao Lower Bound Analysis of Vegetation Height Estimation with Random Volume Over Ground Model and Polarimetric SAR Interferometry","volume":"8","author":"Roueff","year":"2011","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1414","DOI":"10.1109\/LGRS.2013.2294343","article-title":"Invariant Contrast Parameters of PolInSAR Homogenous RVoG Model","volume":"11","author":"Roueff","year":"2014","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Wang, X., Xu, F., and Jin, Y. (2021, January 11\u201316). The Optimum Baseline Analysis for Polinsar Forest Height Mapping. Proceedings of the IEEE Geoscience and Remote Sensing Symposium, Brussels, Belgium.","DOI":"10.1109\/IGARSS47720.2021.9555051"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1879","DOI":"10.1109\/TGRS.2013.2256362","article-title":"Vegetation Height Estimation Precision with Compact PolInSAR and Homogeneous Random Volume Over Ground Model","volume":"52","author":"Arnaubec","year":"2014","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"4126","DOI":"10.1109\/TGRS.2018.2826054","article-title":"Precision of Vegetation Height Estimation Using the Dual-Baseline PolInSAR System and RVoG Model with Temporal Decorrelation","volume":"56","author":"Sportouche","year":"2018","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"950","DOI":"10.1109\/36.175330","article-title":"Decorrelation in interferometric radar echoes","volume":"30","author":"Zebker","year":"1992","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1049\/ip-rsn:20030449","article-title":"Three-stage inversion process for polarimetric SAR interferometry","volume":"150","author":"Cloude","year":"2003","journal-title":"IEEE Proc.-Radar Sonar Navig."},{"key":"ref_33","unstructured":"Garthwaite, P., Jolliffe, I., and Jones, B. (1995). Statistical Inference, Prentice-Hall."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"4833","DOI":"10.1109\/JSTARS.2023.3271186","article-title":"Biomass Estimation and Uncertainty Quantification from Tree Height","volume":"16","author":"Song","year":"2023","journal-title":"IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Olesk, A., Praks, J., Antropov, O., Zalite, K., Arum\u00e4e, T., and Voormansik, K. (2016). Interferometric SAR Coherence Models for Characterization of Hemiboreal Forests Using TanDEM-X Data. Remote Sens., 8.","DOI":"10.3390\/rs8090700"},{"key":"ref_36","unstructured":"Papathanassiou, K.P., and Cloude, S.R. (2003, January 21\u201325). The effect of temporal decorrelation on the inversion of forest parameters from Pol-InSAR data. Proceedings of the IEEE Geoscience and Remote Sensing Symposium, Toulouse, France."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"2880","DOI":"10.1109\/TGRS.2011.2174367","article-title":"A temporal decorrelation model for polarimetric radar interferometers","volume":"50","author":"Lavalle","year":"2012","journal-title":"IEEE Trans. Geosci. Remote Sens."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/22\/5321\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:21:22Z","timestamp":1760131282000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/22\/5321"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,11,10]]},"references-count":37,"journal-issue":{"issue":"22","published-online":{"date-parts":[[2023,11]]}},"alternative-id":["rs15225321"],"URL":"https:\/\/doi.org\/10.3390\/rs15225321","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2023,11,10]]}}}