{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T23:15:54Z","timestamp":1780355754892,"version":"3.54.1"},"reference-count":37,"publisher":"MDPI AG","issue":"22","license":[{"start":{"date-parts":[[2020,11,20]],"date-time":"2020-11-20T00:00:00Z","timestamp":1605830400000},"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>High resolution synthetic aperture radar (SAR) imaging has extensive application value especially in military reconnaissance and disaster monitoring. The motion of the satellite during the transmission and reception of the signal introduces notable errors in the high resolution SAR spotlight mode, which will lead to a defocused SAR image if not handled. To address this problem, an accurate correct echo model based on non-start-stop model is derived to describe the property of the SAR signal in the paper. Then, in the imaging processing, an azimuth-time-varying range frequency modulation rate is used for range compression. The range history and compensation phase are also derived based on the correct echo model. Then, combining the correct echo model and Cartesian factorized backprojection (CFBP) algorithm, a modified CFBP algorithm is proposed for SAR imaging to improve the accuracy and efficiency of processing. Besides, the influence of residual error due to mismatch is analyzed in detail. In the end, the simulation experiment and Gaofen-3 (GF-3) data experiment are carried out to demonstrate the feasibility of the proposed algorithm.<\/jats:p>","DOI":"10.3390\/rs12223807","type":"journal-article","created":{"date-parts":[[2020,11,20]],"date-time":"2020-11-20T09:46:18Z","timestamp":1605865578000},"page":"3807","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["A Modified Cartesian Factorized Backprojection Algorithm Integrating with Non-Start-Stop Model for High Resolution SAR Imaging"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9092-5298","authenticated-orcid":false,"given":"Da","family":"Liang","sequence":"first","affiliation":[{"name":"Space Microwave Remote Sensing System Department, Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100094, China"},{"name":"School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Heng","family":"Zhang","sequence":"additional","affiliation":[{"name":"Space Microwave Remote Sensing System Department, Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100094, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9194-5370","authenticated-orcid":false,"given":"Tingzhu","family":"Fang","sequence":"additional","affiliation":[{"name":"Space Microwave Remote Sensing System Department, Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100094, China"},{"name":"School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Haoyu","family":"Lin","sequence":"additional","affiliation":[{"name":"Space Microwave Remote Sensing System Department, Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100094, China"},{"name":"School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dacheng","family":"Liu","sequence":"additional","affiliation":[{"name":"Space Microwave Remote Sensing System Department, Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100094, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaoxue","family":"Jia","sequence":"additional","affiliation":[{"name":"Space Microwave Remote Sensing System Department, Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100094, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,11,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1109\/MGRS.2013.2248301","article-title":"A tutorial on synthetic aperture radar","volume":"1","author":"Moreira","year":"2013","journal-title":"IEEE Geosci. Remote Sens. Mag."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Jia, H., Wang, Y., Ge, D., Deng, Y., and Wang, R. (2020). Improved offset tracking for predisaster deformation monitoring of the 2018 Jinsha River landslide (Tibet, China). Remote Sens. Environ., 247.","DOI":"10.1016\/j.rse.2020.111899"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"3619","DOI":"10.1109\/TGRS.2019.2958863","article-title":"On the Frequency Dispersion in DBF SAR and Digital Scalloped Beamforming","volume":"58","author":"Zhao","year":"2020","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"3695","DOI":"10.1109\/TGRS.2013.2274821","article-title":"The TerraSAR-X Staring Spotlight Mode Concept","volume":"52","author":"Mittermayer","year":"2014","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Sun, J., Yu, W., and Deng, Y. (2017). The SAR Payload Design and Performance for the GF-3 Mission. Sensors, 17.","DOI":"10.3390\/s17102419"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"49","DOI":"10.5721\/EuJRS20154804","article-title":"Extension of Wavenumber Domain Focusing for spotlight COSMO-SkyMed SAR Data","volume":"48","author":"Lorusso","year":"2015","journal-title":"Eur. J. Remote Sens."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"6003","DOI":"10.1109\/TGRS.2013.2294353","article-title":"On the Processing of Very High Resolution Spaceborne SAR Data","volume":"52","author":"Scheiber","year":"2014","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"4252","DOI":"10.1109\/TGRS.2017.2688728","article-title":"Precise Calibration of Channel Imbalance for Very High Resolution SAR With Stepped Frequency","volume":"55","author":"Wang","year":"2017","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1109\/TGRS.2016.2608423","article-title":"Autofocus Correction of Residual RCM for VHR SAR Sensors With Light-Small Aircraft","volume":"55","author":"Ning","year":"2017","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2112","DOI":"10.1109\/JSTARS.2020.2986862","article-title":"Processing of Very High Resolution GF-3 SAR Spotlight Data With Non-Start\u2013Stop Model and Correction of Curved Orbit","volume":"13","author":"Liang","year":"2020","journal-title":"IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1993","DOI":"10.1109\/36.951090","article-title":"Spotlight SAR data focusing based on a two-step processing approach","volume":"39","author":"Lanari","year":"2001","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"646","DOI":"10.1137\/08074026X","article-title":"On the Use of Start-Stop Approximation for Spaceborne SAR Imaging","volume":"2","author":"Tsynkov","year":"2009","journal-title":"Siam J. Imaging Sci."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Yu, Z., Wang, S., and Li, Z. (2016). An Imaging Compensation Algorithm for Spaceborne High-Resolution SAR Based on a Continuous Tangent Motion Model. Remote Sens., 8.","DOI":"10.3390\/rs8030223"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2949","DOI":"10.1109\/TAES.2011.6034676","article-title":"Efficient Time-Domain Image Formation with Precise Topography Accommodation for General Bistatic SAR Configurations","volume":"47","author":"Prats","year":"2011","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1505","DOI":"10.1109\/TGRS.2015.2481923","article-title":"Processing of Very High Resolution Spaceborne Sliding Spotlight SAR Data Using Velocity Scaling","volume":"54","author":"Yuan","year":"2016","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"770","DOI":"10.1109\/TGRS.2009.2027701","article-title":"Processing of Sliding Spotlight and TOPS SAR Data Using Baseband Azimuth Scaling","volume":"48","author":"Prats","year":"2010","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"396","DOI":"10.1109\/LGRS.2010.2078486","article-title":"Time-Domain Reconstruction Algorithms for FMCW-SAR","volume":"8","author":"Ribalta","year":"2011","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_18","first-page":"505","article-title":"Convolution backprojection image reconstruction for spotlight mode synthetic aperture radar","volume":"1","author":"Desai","year":"1992","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2035","DOI":"10.1109\/JSTARS.2013.2238891","article-title":"Streaming BP for Non-Linear Motion Compensation SAR Imaging Based on GPU","volume":"6","author":"Shi","year":"2013","journal-title":"IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens."},{"key":"ref_20","first-page":"368","article-title":"High-resolution Slide Spotlight SAR Imaging by BP Algorithm and Heterogeneous Parallel Implementation","volume":"6","author":"Tang","year":"2017","journal-title":"J. Radars"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1109\/MSP.2009.935383","article-title":"Synthetic aperture radar processing with GPGPU","volume":"27","author":"Bisceglie","year":"2010","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_22","unstructured":"Yegulalp, A.F. (1999, January 22). Fast backprojection algorithm for synthetic aperture radar. Proceedings of the 1999 IEEE Radar Conference, Waltham, MA, USA."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"760","DOI":"10.1109\/TAES.2003.1238734","article-title":"Synthetic aperture radar processing using fast factorized back-projection","volume":"39","author":"Ulander","year":"2003","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Zhang, H., Tang, J., Wang, R., Deng, Y., Wang, W., and Li, N. (2018). An Accelerated Backprojection Algorithm for Monostatic and Bistatic SAR Processing. Remote Sens., 10.","DOI":"10.3390\/rs10010140"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1160","DOI":"10.1109\/JSEN.2017.2780164","article-title":"Cartesian Factorized Backprojection Algorithm for High-Resolution Spotlight SAR Imaging","volume":"18","author":"Dong","year":"2018","journal-title":"IEEE Sens. J."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"902","DOI":"10.1109\/LGRS.2018.2885196","article-title":"A Modified Cartesian Factorized Back-Projection Algorithm for Highly Squint Spotlight Synthetic Aperture Radar Imaging","volume":"16","author":"Luo","year":"2019","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1508","DOI":"10.1109\/JSTARS.2019.2907138","article-title":"A New Fast Factorized Back Projection Algorithm for Bistatic Forward-Looking SAR Imaging Based on Orthogonal Elliptical Polar Coordinate","volume":"12","author":"Zhou","year":"2019","journal-title":"IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1080","DOI":"10.1109\/LGRS.2012.2230243","article-title":"Fast Backprojection Algorithm for Bistatic SAR Imaging","volume":"10","author":"Shao","year":"2013","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1460","DOI":"10.1109\/LGRS.2013.2295326","article-title":"A Fast BP Algorithm With Wavenumber Spectrum Fusion for High-Resolution Spotlight SAR Imaging","volume":"11","author":"Zhang","year":"2014","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1049\/ip-rsn:20045110","article-title":"Evaluation of angular interpolation kernels in fast back-projection SAR processing","volume":"153","author":"Frolind","year":"2006","journal-title":"IEE Proc. Radar Sonar Navig."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Dong, Q., Yang, Z., Sun, G., and Xing, M. (2016, January 10\u201315). Cartesian factorized backprojection algorithm for synthetic aperture radar. Proceedings of the IEEE Geoscience and Remote Sensing Symposium, Beijing, China.","DOI":"10.1109\/IGARSS.2016.7729272"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1244","DOI":"10.1109\/LGRS.2018.2829483","article-title":"An Autofocus Cartesian Factorized Backprojection Algorithm for Spotlight Synthetic Aperture Radar Imaging","volume":"15","author":"Luo","year":"2018","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_33","unstructured":"Chen, X., Sun, G., Xing, M., Li, B., Yang, J., and Bao, Z. (2020). Ground Cartesian Back-Projection Algorithm for High Squint Diving TOPS SAR Imaging. IEEE Trans. Geosci. Remote Sens., 1\u201316."},{"key":"ref_34","unstructured":"Cumming, I.G., and Wong, F.H. (2005). Digital Signal Processing of Synthetic Aperture Radar Data: Algorithms and Implementation, Artech House."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"933","DOI":"10.1109\/TGRS.2011.2162243","article-title":"Echo Model Analyses and Imaging Algorithm for High-Resolution SAR on High-Speed Platform","volume":"50","author":"Yan","year":"2012","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1056","DOI":"10.1109\/LGRS.2019.2891510","article-title":"Echo Model Without Stop-and-Go Approximation for Bistatic SAR With Maneuvers","volume":"16","author":"Zhang","year":"2019","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Zhang, F., Li, G., Li, W., Hu, W., and Hu, Y. (2016). Accelerating Spaceborne SAR Imaging Using Multiple CPU\/GPU Deep Collaborative Computing. Sensors, 16.","DOI":"10.3390\/s16040494"}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/12\/22\/3807\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:35:02Z","timestamp":1760178902000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/12\/22\/3807"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,11,20]]},"references-count":37,"journal-issue":{"issue":"22","published-online":{"date-parts":[[2020,11]]}},"alternative-id":["rs12223807"],"URL":"https:\/\/doi.org\/10.3390\/rs12223807","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,11,20]]}}}