{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T01:41:43Z","timestamp":1773106903171,"version":"3.50.1"},"reference-count":36,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,1,6]],"date-time":"2021-01-06T00:00:00Z","timestamp":1609891200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62001062, 61971075, and 61871305"],"award-info":[{"award-number":["62001062, 61971075, and 61871305"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"the Opening Project of Guangxi Wireless Broadband Communication and Signal Processing Key Laboratory","award":["GXKL06200214, and GXKL06200205"],"award-info":[{"award-number":["GXKL06200214, and GXKL06200205"]}]},{"name":"Key Project of Application and Development of Chongqing","award":["cstc2019jscx-fxydX0049"],"award-info":[{"award-number":["cstc2019jscx-fxydX0049"]}]},{"name":"Pre-Research Fund Project","award":["61404130219"],"award-info":[{"award-number":["61404130219"]}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["2019CDQYTX012"],"award-info":[{"award-number":["2019CDQYTX012"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Ground moving targets will typically be defocused because of the range migration (RM) and Doppler frequency migration (DFM) caused by the unknown relative motions between the platform of synthetic aperture radar (SAR) and the ground moving targets. The received signal of the ground moving target easily exhibits the Doppler ambiguity, and the Doppler ambiguity leads to the refocusing difficulty of ground moving targets. To address these problems, a SAR refocusing method of ground moving targets with Doppler ambiguity based on modified second-order keystone transform (MSOKT) and keystone transform (KT) is presented in this paper. Firstly, the second-order phase is separated by the time reversing process. Secondly, MSOKT is performed to compensate the range curvature migration and DFM, and then the coefficient of the second-order phase is estimated. Finally, a well-refocused result of the moving target is achieved after KT and the estimated Doppler ambiguity number are used to eliminate residual range walk migration. The proposed method can accurately remove RM and DFM and effectively focus the moving targets without residual correction errors. Moreover, the effects of Doppler ambiguity (including Doppler center blur and spectrum split) and blind speed sidelobe are further avoided. On the basis of the analysis of cross-term for the multiple target case, the identification strategy of spurious peak of cross-term is proposed. Additionally, the developed method can be sped up by nonuniform fast Fourier transform without the interpolation operation. The effectiveness of the proposed method is verified by both airborne and spaceborne real data processing results.<\/jats:p>","DOI":"10.3390\/rs13020177","type":"journal-article","created":{"date-parts":[[2021,1,6]],"date-time":"2021-01-06T20:45:42Z","timestamp":1609965942000},"page":"177","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":21,"title":["Refocusing of Ground Moving Targets with Doppler Ambiguity Using Keystone Transform and Modified Second-Order Keystone Transform for Synthetic Aperture Radar"],"prefix":"10.3390","volume":"13","author":[{"given":"Jun","family":"Wan","sequence":"first","affiliation":[{"name":"School of Microelectronics and Communication Engineering, Chongqing University, Chongqing 400044, China"},{"name":"Chongqing Key Laboratory of Space Information Network and Intelligent Information Fusion, Chongqing University, Chongqing 400044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaoheng","family":"Tan","sequence":"additional","affiliation":[{"name":"School of Microelectronics and Communication Engineering, Chongqing University, Chongqing 400044, China"},{"name":"Chongqing Key Laboratory of Space Information Network and Intelligent Information Fusion, Chongqing University, Chongqing 400044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2590-7704","authenticated-orcid":false,"given":"Zhanye","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Microelectronics and Communication Engineering, Chongqing University, Chongqing 400044, China"},{"name":"Chongqing Key Laboratory of Space Information Network and Intelligent Information Fusion, Chongqing University, Chongqing 400044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dong","family":"Li","sequence":"additional","affiliation":[{"name":"School of Microelectronics and Communication Engineering, Chongqing University, Chongqing 400044, China"},{"name":"Chongqing Key Laboratory of Space Information Network and Intelligent Information Fusion, Chongqing University, Chongqing 400044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qinghua","family":"Liu","sequence":"additional","affiliation":[{"name":"Guangxi Wireless Broadband Communication and Signal Processing Key Laboratory, Guilin University of Electronic Technology, Guilin 541004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yu","family":"Zhou","sequence":"additional","affiliation":[{"name":"National Laboratory of Radar Signal Processing, Xidian University, Xi\u2019an 710071, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Linrang","family":"Zhang","sequence":"additional","affiliation":[{"name":"National Laboratory of Radar Signal Processing, Xidian University, Xi\u2019an 710071, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,1,6]]},"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","first-page":"1637","DOI":"10.3390\/rs11141637","article-title":"Micro-motion estimation of maritime targets using pixel tracking in Cosmo-Skymed synthetic aperture radar data-an operative assessment","volume":"11","author":"Filippo","year":"2019","journal-title":"Remote Sens."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Tang, S., Zhang, L., and So, H.C. (2018). Focusing high-resolution highly-squinted airborne SAR data with maneuvers. Remote Sens., 10.","DOI":"10.3390\/rs10060862"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Li, X., Zhou, S., and Yang, L. (2020). A new fast factorized back-projection algorithm with reduced topography sensibility for missile-borne SAR focusing with diving movement. Remote Sens., 12.","DOI":"10.3390\/rs12162616"},{"key":"ref_5","unstructured":"Cumming, I.G., and Wong, F.H. (2005). Digital Processing of Synthetic Aperture Radar Data: Algorithm and Implementation, Artech House."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Qin, M., Li, D., Tang, X., Cao, Z., Li, W., and Xu, L. (2019). A fast high-resolution imaging algorithm for helicopter-borne rotating array SAR based on 2-D chirp-z transform. Remote Sens., 11.","DOI":"10.3390\/rs11141669"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1774","DOI":"10.1109\/TGRS.2017.2768243","article-title":"GMTI and parameter estimation for MIMO SAR system via fast interferometry RPCA method","volume":"56","author":"Huang","year":"2018","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Chen, Z., Zhou, Y., Zhang, L., Lin, C., Huang, Y., and Tang, S. (2018). Ground moving target imaging and analysis for near-space hypersonic vehicle-borne synthetic aperture radar system with squint angle. Remote Sens., 10.","DOI":"10.3390\/rs10121966"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Rahmanizadeh, A., and Amini, J. (2017). An integrated method for simulation of synthetic aperture radar (SAR) raw data in moving target detection. Remote Sens., 9.","DOI":"10.3390\/rs9101009"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1049\/el.2018.7263","article-title":"General range model for multi-channel SAR\/GMTI with curvilinear flight trajectory","volume":"55","author":"Chen","year":"2019","journal-title":"Electron. Lett."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"5015","DOI":"10.1109\/JSTARS.2015.2450019","article-title":"Simultaneous high-resolution wide-swath SAR imaging and ground moving target indication: Processing approaches and system concepts","volume":"8","author":"Baumgartner","year":"2015","journal-title":"IEEE J. Sel. Topics Appl. Earth Observ. Remote Sens."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"528","DOI":"10.1049\/iet-spr.2018.5225","article-title":"Ground moving target focusing and motion parameter estimation method via MSOKT for synthetic aperture radar","volume":"13","author":"Wan","year":"2019","journal-title":"IET Signal Process."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1109\/TCI.2018.2855436","article-title":"Refocusing and motion parameter estimation for ground moving targets based on improved axis rotation-time reversal transform","volume":"4","author":"Huang","year":"2018","journal-title":"IEEE Trans. Comput. Imag."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"472","DOI":"10.1049\/iet-spr.2018.5418","article-title":"A non-adaptive space-time clutter canceller for multi-channel synthetic aperture radar","volume":"13","author":"Chen","year":"2019","journal-title":"IET Signal Process."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"966","DOI":"10.1109\/TGRS.2012.2204889","article-title":"Robust ground moving-target imaging using deramp-Keystone processing","volume":"51","author":"Sun","year":"2013","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"462","DOI":"10.1109\/TGRS.2010.2053848","article-title":"Ground moving targets imaging algorithm for synthetic aperture radar","volume":"49","author":"Zhu","year":"2011","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Zeng, H., Chen, J., Wang, P., Yang, W., and Liu, W. (2018). 2-D coherent integration processing and detecting of aircrafts using GNSS-based passive radar. Remote Sens., 10.","DOI":"10.3390\/rs10071164"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"646","DOI":"10.1049\/iet-rsn.2016.0262","article-title":"Coherent method for ground-moving target indication and velocity estimation using Hough transform","volume":"11","author":"Oveis","year":"2017","journal-title":"IET Radar Sonar Navig."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"188","DOI":"10.1109\/7.745691","article-title":"SAR imaging of moving targets","volume":"35","author":"Perry","year":"1999","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"774","DOI":"10.1049\/cje.2016.06.009","article-title":"High accuracy velocity measurement based on keystone transform using entropy minimization","volume":"25","author":"Dai","year":"2016","journal-title":"Chin. J. Electron."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1109\/LGRS.2006.882147","article-title":"A keystone transform without interpolation for SAR ground moving-target imaging","volume":"4","author":"Zhu","year":"2007","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"902","DOI":"10.1049\/iet-rsn.2010.0304","article-title":"Imaging moving targets using the second-order keystone transform","volume":"5","author":"Kirkland","year":"2011","journal-title":"IET Radar Sonar Navig."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1049\/iet-rsn:20060040","article-title":"Approach for single channel SAR ground moving target imaging and motion parameter estimation","volume":"1","author":"Zhou","year":"2007","journal-title":"IET Radar Sonar Navig."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"573","DOI":"10.1109\/LGRS.2008.2000621","article-title":"Doppler keystone transform: An approach suitable for parallel implementation of SAR moving target imaging","volume":"5","author":"Li","year":"2008","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_25","first-page":"1125","article-title":"Detection of a low observable sea-surface target with micromotion via Radon-linear canonical transform","volume":"11","author":"Chen","year":"2014","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"939","DOI":"10.1109\/TSP.2013.2297682","article-title":"Maneuvering target detection via Radon-fractional Fourier transform-based long-time coherent integration","volume":"62","author":"Chen","year":"2014","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1467","DOI":"10.1109\/LSP.2015.2390777","article-title":"Coherent integration for maneuvering target detection based on Radon-Lv\u2019s distribution","volume":"22","author":"Li","year":"2015","journal-title":"IEEE Signal Process."},{"key":"ref_28","unstructured":"Wan, J., Chen, Z., Zhou, Y., Li, D., Huang, Y., and Zhang, L. (October, January 26). Ground moving target imaging based on MSOKT and KT for synthetic aperture radar. Proceedings of the IEEE International Geoscience Remote Sensing Symposium, HI, USA."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1109\/TCI.2015.2510499","article-title":"Parameter estimation of ground moving targets based on SKT-DLVT processing","volume":"2","author":"Tian","year":"2016","journal-title":"IEEE Trans. Comput. Imag."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"4977","DOI":"10.1109\/TSP.2008.927457","article-title":"Subspace-based algorithm for parameter estimation of polynomial phase signals","volume":"56","author":"Wu","year":"2008","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"336","DOI":"10.1109\/TGRS.2016.2606437","article-title":"An approach for refocusing of ground moving target without motion parameter estimation","volume":"55","author":"Huang","year":"2017","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"732","DOI":"10.1049\/iet-rsn.2014.0192","article-title":"Approach for space-based radar maneuvering target detection and high-order motion parameter estimation","volume":"9","author":"Huang","year":"2015","journal-title":"IET Radar Sonar Navig."},{"key":"ref_33","unstructured":"DiPietro, R.C. (1992, January 26\u201328). Extended factored space-time processing for airborne radar systems. Proceedings of the Twenty-Sixth Asilomar Conference on Signals, Systems & Computers, Pacific Grove, CA, USA."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1109\/75.650975","article-title":"An accurate algorithm for nonuniform fast Fourier transforms (NUFFT\u2019s)","volume":"8","author":"Liu","year":"1998","journal-title":"IEEE Microw. Guided Wave Lett."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1462","DOI":"10.1109\/TGRS.2006.870412","article-title":"Two-dimensional and three-dimensional NUFFT migration method for landmine detection using ground-penetrating radar","volume":"44","author":"Song","year":"2006","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Liu, Q.H., Nguyen, N., and Tang, X.Y. (1998, January 6\u201310). Accurate algorithms for nonuniform fast forward and inverse Fourier transforms and their applications. Proceedings of the IEEE International Geoscience Remote Sensing Symposium, Seattle, DC, USA.","DOI":"10.1109\/IGARSS.1998.702881"}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/2\/177\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:07:49Z","timestamp":1760159269000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/2\/177"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1,6]]},"references-count":36,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2021,1]]}},"alternative-id":["rs13020177"],"URL":"https:\/\/doi.org\/10.3390\/rs13020177","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1,6]]}}}