{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:02:44Z","timestamp":1760241764775,"version":"build-2065373602"},"reference-count":28,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2018,8,26]],"date-time":"2018-08-26T00:00:00Z","timestamp":1535241600000},"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":["61771015 and 61501068"],"award-info":[{"award-number":["61771015 and 61501068"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Key R&amp;D Program of China","award":["2016YFE0200400"],"award-info":[{"award-number":["2016YFE0200400"]}]},{"name":"Key R&amp;D Program of ShanXi Province","award":["2017KW-ZD-12"],"award-info":[{"award-number":["2017KW-ZD-12"]}]},{"name":"Innovative Research Group of National Natural Science Foundation of China","award":["61621005"],"award-info":[{"award-number":["61621005"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The inverse synthetic aperture radar (ISAR) imaging for targets with complex motions has always been a challenging task due to the time-varying Doppler parameter, especially at the low signal-to-noise ratio (SNR) condition. In this paper, an efficient ISAR imaging algorithm for maneuvering targets based on a noise-resistance bilinear coherent integration is developed without the parameter estimation. First, the received signals of the ISAR in a range bin are modelled as a multicomponent quadratic frequency-modulated (QFM) signal after the translational motion compensation. Second, a novel quasi-time-frequency representation noise-resistance bilinear Radon-cubic phase function (CPF)-Fourier transform (RCFT) is proposed, which is based on the coherent integration of the energy of auto-terms along the slope line trajectory. In doing so, the RCFT also effectively suppresses the cross-terms and spurious peaks interference at no expense of the time-frequency resolution loss. Third, the cross-range positions of target\u2019s scatters in ISAR image are obtained via a simple maximization projection from the RCFT result to the Doppler centroid axis, and the final high-resolution ISAR image is thus produced by regrouping all the range-Doppler frequency centroids. Compared with the existing time-frequency analysis-based and parameter estimation-based ISAR imaging algorithms, the proposed method presents the following features: (1) Better cross-term interference suppression at no time-frequency resolution loss; (2) computationally efficient without estimating the parameters of each scatters; (3) higher signal processing gain because of 2-D coherent integration realization and its bilinear function feature. The simulation results are provided to demonstrate the performance of the proposed method.<\/jats:p>","DOI":"10.3390\/s18092814","type":"journal-article","created":{"date-parts":[[2018,8,27]],"date-time":"2018-08-27T10:56:04Z","timestamp":1535367364000},"page":"2814","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["An Efficient ISAR Imaging of Targets with Complex Motions Based on a Quasi-Time-Frequency Analysis Bilinear Coherent Algorithm"],"prefix":"10.3390","volume":"18","author":[{"given":"Cao","family":"Zeng","sequence":"first","affiliation":[{"name":"National Laboratory of Radar Signal Processing, Xidian University, Xian 710071, China"}]},{"given":"Mengyi","family":"Qin","sequence":"additional","affiliation":[{"name":"Center of Communication and Tracking Telemetering Command, Chongqing University, Chongqing 400044, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2441-852X","authenticated-orcid":false,"given":"Dong","family":"Li","sequence":"additional","affiliation":[{"name":"Center of Communication and Tracking Telemetering Command, Chongqing University, Chongqing 400044, China"},{"name":"Key Laboratory of Complex System Safety and Control, Ministry of Education, Chongqing University, Chongqing 400044, China"},{"name":"Guangxi Key Laboratory of Wireless Wideband Communication and Signal Processing, Guilin University of Electronic Technology 541004, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2069-0390","authenticated-orcid":false,"given":"Hongqing","family":"Liu","sequence":"additional","affiliation":[{"name":"Chongqing Key Laboratory of Mobile Communications Technology, Chongqing University of Posts and Telecommunications, Chongqing 400065, China"}]},{"given":"Yi","family":"Chai","sequence":"additional","affiliation":[{"name":"Key Laboratory of Complex System Safety and Control, Ministry of Education, Chongqing University, Chongqing 400044, China"}]}],"member":"1968","published-online":{"date-parts":[[2018,8,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"4053","DOI":"10.1109\/JSEN.2015.2409884","article-title":"Inverse synthetic aperture radar imaging of nonuniformly rotating target based on the parameters estimation of multicomponent quadratic frequency-modulated signals","volume":"15","author":"Wang","year":"2012","journal-title":"IEEE Sens. J."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1109\/TGRS.2011.2160185","article-title":"A novel method for imaging of group targets moving in a formation","volume":"50","author":"Bai","year":"2012","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"4775","DOI":"10.1109\/JSTARS.2015.2460734","article-title":"ISAR imaging of targets with complex motions based on modified Lv\u2019s distribution for cubic phase signal","volume":"8","author":"Li","year":"2015","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"doi-asserted-by":"crossref","unstructured":"Sadjadi, F. (2014, January 19\u201323). New comparative experiments in range migration mitigation methods using polarimetric inverse synthetic aperture radar signatures of small boats. Proceedings of the IEEE Radar Conference, Cincinnati, OH, USA.","key":"ref_4","DOI":"10.1109\/RADAR.2014.6875664"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"941","DOI":"10.1109\/5.30749","article-title":"Time-frequency distributions-a review","volume":"77","author":"Cohen","year":"1989","journal-title":"Proc. IEEE"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"486","DOI":"10.1109\/7.670330","article-title":"Joint time-frequency transform for radar range Doppler imaging","volume":"34","author":"Chen","year":"1998","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2971","DOI":"10.1109\/JSTARS.2014.2301158","article-title":"ISAR imaging of maneuvering target based on the local polynomial Wigner distribution and integrated high-order ambiguity function for cubic phase signal model","volume":"7","author":"Wang","year":"2014","journal-title":"IEEE J. Sel.Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"4727","DOI":"10.1109\/TGRS.2015.2408350","article-title":"ISAR imaging of nonuniformly rotating target based on a fast parameter estimation algorithm of cubic phase signal","volume":"53","author":"Zheng","year":"2015","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"5688","DOI":"10.1109\/JSTARS.2016.2543233","article-title":"An ISAR imaging algorithm for maneuvering targets with low SNR based on parameter estimation of multicomponent quadratic FM signals and nonuniform FFT","volume":"9","author":"Li","year":"2016","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"262","DOI":"10.1049\/ip-rsn:19982220","article-title":"Time-varying spectral analysis for radar imaging of maneuvering targets","volume":"145","author":"Chen","year":"1998","journal-title":"IEEE Proc. Radar Sonar Navig."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1789","DOI":"10.1109\/8.901267","article-title":"Efficient radar target classification using adaptive joint time-frequency processing","volume":"48","author":"Kim","year":"2000","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1091","DOI":"10.1109\/7.953260","article-title":"Time-frequency approaches to ISAR imaging of maneuvering targets and their limitations","volume":"37","author":"Bao","year":"2001","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1880","DOI":"10.1109\/83.974573","article-title":"High-resolution ISAR imaging of maneuvering targets by means of the range instantaneous Doppler technique: Modeling and performance analysis","volume":"10","author":"Berizzi","year":"2001","journal-title":"IEEE Trans. Image Process."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1518","DOI":"10.1109\/TGRS.2009.2032296","article-title":"ISAR imaging of maneuvering targets based on the L-class of fourth-order complex-lag PWVD","volume":"48","author":"Wang","year":"2010","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1109\/TIP.2009.2032892","article-title":"ISAR imaging of maneuvering targets based on the range centroid Doppler technique","volume":"19","author":"Lv","year":"2010","journal-title":"IEEE Trans. Image Process."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1049\/iet-rsn:20080003","article-title":"New ISAR imaging algorithm based on modified Wigner-Ville distribution","volume":"3","author":"Xing","year":"2009","journal-title":"IET Radar Sonar Navig."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1109\/TSP.2003.821097","article-title":"A fast algorithm for estimating the parameters of a quadratic FM signal","volume":"52","year":"2004","journal-title":"IEEE Trans. Signal Process."},{"unstructured":"Wang, P., and Yang, J.Y. (2006, January 4\u20138). Parameter estimation of multicomponent quadratic FM signals using computationally efficient Radon-CPF transform. Proceedings of the 14th European Signal Processing Conference, Florence, Italy.","key":"ref_18"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1137\/S1064827597325712","article-title":"The regular Fourier matrices and nonuniform fast Fourier transforms","volume":"21","author":"Nguyen","year":"1999","journal-title":"SIAM J. Sci. Comput."},{"key":"ref_20","first-page":"1105","article-title":"Ground maneuvering target imaging and high-order motion parameter estimation based on second-order Keystone and generalized Hough-HAF transform","volume":"53","author":"Huang","year":"2015","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1186","DOI":"10.1109\/TAES.2011.5751251","article-title":"Radon\u2013Fourier transform for radar target detection, I: Generalized Doppler filter bank","volume":"47","author":"Xu","year":"2011","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_22","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_23","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/1687-6180-2013-33","article-title":"Translational motion compensation for ISAR imaging under low SNR by minimum entropy","volume":"2013","author":"Zhang","year":"2013","journal-title":"EURASIP J. Adv. Signal Process."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"5146","DOI":"10.1109\/JSTARS.2015.2491307","article-title":"Adaptive translational motion compensation method for ISAR imaging under low SNR based on particle swarm optimization","volume":"8","author":"Liu","year":"2015","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2140","DOI":"10.1109\/TAES.2017.2683599","article-title":"A robust translational motion compensation method for ISAR imaging based on Keystone transform and fractional Fourier transform under low SNR environment","volume":"53","author":"Li","year":"2017","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"586","DOI":"10.1049\/iet-rsn.2009.0027","article-title":"Generalization of inverse synthetic aperture radar autofocusing methods based on the minimization of the Renyi entropy","volume":"4","author":"Datcu","year":"2010","journal-title":"IET Radar Sonar Navig."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1049\/ip-rsn:20045123","article-title":"Contrast maximization based technique for 2-D. ISAR autofocusing","volume":"152","author":"Martorella","year":"2005","journal-title":"IET Proc. Radar Sonar Navig."},{"doi-asserted-by":"crossref","unstructured":"Liu, H.Q., Li, D., Zhou, Y., and Truong, T.-K. (2018). Simultaneous radio frequency and wideband interference suppression in SAR signals via sparsity exploitation in time-frequency Domain. IEEE Trans. Geosci. Remote Sens., 1\u201314.","key":"ref_28","DOI":"10.1109\/TGRS.2018.2825459"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/9\/2814\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:21:13Z","timestamp":1760196073000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/9\/2814"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,8,26]]},"references-count":28,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2018,9]]}},"alternative-id":["s18092814"],"URL":"https:\/\/doi.org\/10.3390\/s18092814","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2018,8,26]]}}}