{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,6]],"date-time":"2025-12-06T05:00:04Z","timestamp":1764997204431,"version":"build-2065373602"},"reference-count":38,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2018,12,28]],"date-time":"2018-12-28T00:00:00Z","timestamp":1545955200000},"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>In the case of low frequencies (e.g., P-band) radar observations, the Gaussian Vertical Backscatter (GVB) model, a model that takes into account the vertical heterogeneity of the wave-canopy interactions, can describe the forest vertical backscatter profile (VBP) more accurately. However, the GVB model is highly complex, seriously reducing the inversion efficiency because of a number of variables. Given that concern, this paper proposes a constrained Gaussian Vertical Backscatter (CGVB) model to reduce the complexity of the GVB model by establishing a constraint relationship between forest height and the backscattering vertical fluctuation (BVF) of the GVB model. The CGVB model takes into account the influence of incidence angle on scattering mechanisms. The BVF of VBP described by the CGVB model is expressed with forest height and a polynomial function of incidence angle. In order to build the CGVB model, this paper proposes the supervised learning based on RANSAC (SLBR). The proposed SLBR method used forest height as a prior knowledge to determine the function of incidence angle in the CGVB model. In this process, the Random Sample Consensus (RANSAC) method is applied to perform function fitting. Before building the CGVB model, iterative weighted complex least squares (IWCLS) is employed to extract the required volume coherence. Based on the CGVB model, forest height estimation was obtained by nonlinear least squares optimization. E-SAR P-band polarimetric interferometric synthetic aperture radar (Pol-InSAR) data acquired during the BIOSAR 2008 campaign was used to test the performance of the proposed CGVB model. It can be observed that, compared with Random Volume over Ground (RVoG) model, the proposed CGVB model improves the estimation accuracy of the areas with incidence angle less than     0.8     rad and less than     0.6     rad by     28.57 %     and     40.35 %    , respectively.<\/jats:p>","DOI":"10.3390\/rs11010042","type":"journal-article","created":{"date-parts":[[2018,12,28]],"date-time":"2018-12-28T11:52:42Z","timestamp":1545997962000},"page":"42","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Forest Height Estimation Based on Constrained Gaussian Vertical Backscatter Model Using Multi-Baseline P-Band Pol-InSAR Data"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6650-8507","authenticated-orcid":false,"given":"Xiaofan","family":"Sun","sequence":"first","affiliation":[{"name":"Science and Technology on Microwave Imaging Laboratory, Institute of Electronics, Chinese Academy of Sciences, Beijing 100190, China"},{"name":"School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bingnan","family":"Wang","sequence":"additional","affiliation":[{"name":"Science and Technology on Microwave Imaging Laboratory, Institute of Electronics, Chinese Academy of Sciences, Beijing 100190, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Maosheng","family":"Xiang","sequence":"additional","affiliation":[{"name":"Science and Technology on Microwave Imaging Laboratory, Institute of Electronics, Chinese Academy of Sciences, Beijing 100190, China"},{"name":"School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4785-5132","authenticated-orcid":false,"given":"Shuai","family":"Jiang","sequence":"additional","affiliation":[{"name":"Institute of Spacecraft System Engineering (ISSE), China Academy of Space Technology (CAST), Beijing 100094, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7489-9835","authenticated-orcid":false,"given":"Xikai","family":"Fu","sequence":"additional","affiliation":[{"name":"Science and Technology on Microwave Imaging Laboratory, Institute of Electronics, Chinese Academy of Sciences, Beijing 100190, China"},{"name":"School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,12,28]]},"reference":[{"key":"ref_1","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_2","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_3","doi-asserted-by":"crossref","first-page":"3379","DOI":"10.1109\/TGRS.2009.2022947","article-title":"Forest biophysical parameter estimation using l- and p-band polarimetric sar data","volume":"47","author":"Garestier","year":"2009","journal-title":"IEEE Trans. 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