{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:05:37Z","timestamp":1760144737312,"version":"build-2065373602"},"reference-count":28,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2024,5,18]],"date-time":"2024-05-18T00:00:00Z","timestamp":1715990400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["62301091","62371078","2022M710533","2022M710535","02140011044134","CSTB2022NSCQ-MSX1156"],"award-info":[{"award-number":["62301091","62371078","2022M710533","2022M710535","02140011044134","CSTB2022NSCQ-MSX1156"]}]},{"name":"Chinese Postdoctoral Science Foundation","award":["62301091","62371078","2022M710533","2022M710535","02140011044134","CSTB2022NSCQ-MSX1156"],"award-info":[{"award-number":["62301091","62371078","2022M710533","2022M710535","02140011044134","CSTB2022NSCQ-MSX1156"]}]},{"name":"Starting Research Fund from Chongqing University","award":["62301091","62371078","2022M710533","2022M710535","02140011044134","CSTB2022NSCQ-MSX1156"],"award-info":[{"award-number":["62301091","62371078","2022M710533","2022M710535","02140011044134","CSTB2022NSCQ-MSX1156"]}]},{"name":"Natural Science Foundation Project of Chongqing","award":["62301091","62371078","2022M710533","2022M710535","02140011044134","CSTB2022NSCQ-MSX1156"],"award-info":[{"award-number":["62301091","62371078","2022M710533","2022M710535","02140011044134","CSTB2022NSCQ-MSX1156"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>This paper addresses the problem of weak maneuvering target detection in the space-based bistatic radar system through long-time coherent integration (LTCI). The space-based bistatic radar is vulnerable to the high-order range migration (RM) and Doppler frequency migration (DFM), since the target, the receiver and the transmitter all can play fast movement independently. To correct high- order RM and DFM, this usually involves joint high-dimensional parameter searching, incurring a large computational burden. In our previous work, a dual-scale (DS) decomposition of motion parameters was proposed, in which the optimal GRFT is conditionally decoupled into two cascade procedures called the modified generalized inverse Fourier transform (GIFT) and generalized Fourier transform (GFT), resulting in the DS-GRFT detector. However, even if the DS-GRFT detector preserves the superior performance and dramatically decreases the complexity, high-dimensional searching is still required. In this paper, by analyzing the structure of the DS-GRFT detector, we further designed a conditioned cubic phase function (CCPF) tailored to the range\u2013slow-time signal after GIFT, breaking the joint high-dimensional searching into independent one-dimensional searching. Then, by connecting the proposed CCPF with the GIFT, we achieved a new LTCI detector called the DS-GIFT-CCPF detector, which obtained a significant computational cost reduction with acceptable performance loss, as demonstrated in numerical experiments.<\/jats:p>","DOI":"10.3390\/rs16101798","type":"journal-article","created":{"date-parts":[[2024,5,20]],"date-time":"2024-05-20T03:36:42Z","timestamp":1716176202000},"page":"1798","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Long-Time Coherent Integration for the Spatial-Based Bistatic Radar Based on Dual-Scale Decomposition and Conditioned CPF"],"prefix":"10.3390","volume":"16","author":[{"given":"Suqi","family":"Li","sequence":"first","affiliation":[{"name":"School of Micro-Electronics and Communication Engineering, Chongqing University, Chongqing 401331, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yihan","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Micro-Electronics and Communication Engineering, Chongqing University, Chongqing 401331, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yanfeng","family":"Liang","sequence":"additional","affiliation":[{"name":"China Academy of Electronics Information Technology, Beijing 100041, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bailu","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Micro-Electronics and Communication Engineering, Chongqing University, Chongqing 401331, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,5,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2493","DOI":"10.1109\/TGRS.2008.917599","article-title":"Focusing bistatic SAR data using the nonlinear chirp scaling algorithm","volume":"46","author":"Wong","year":"2008","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1109\/TAES.2017.2739900","article-title":"Maritime moving target indication using passive GNSS-based bistatic radar","volume":"54","author":"Ma","year":"2018","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_3","unstructured":"Feng, W., Wei, W., and Liu, F. (2015, January 14\u201316). Modefied keystone processing algorithm for the space-based bistatic radar systems. Proceedings of the IET International Radar Conference 2015, Hangzhou, China."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"465","DOI":"10.1109\/36.214923","article-title":"Spacecraft studies of planetary surfaces using bistatic radar","volume":"31","author":"Simpson","year":"1993","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_5","first-page":"1","article-title":"Long time coherent integration algorithm for high-speed maneuvering target detection using space-based bistatic radar","volume":"60","author":"Zhang","year":"2022","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"6190","DOI":"10.1109\/TSP.2012.2217137","article-title":"Radar maneuvering target motion estimation based on generalized Radon-Fourier transform","volume":"60","author":"Xu","year":"2012","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_7","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_8","first-page":"6190","article-title":"Radon-Fourier transform for radar target detection (III): Optimality and fast implementations","volume":"60","author":"Xu","year":"2012","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1186","DOI":"10.1109\/TAES.2011.5751251","article-title":"Radon-Fourier transform (RFT) for radar target detection I: Generalized Doppler filter bank","volume":"47","author":"Xu","year":"2011","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_10","first-page":"6190","article-title":"Detection of a low observable sea-surface target with micromotion via Radon-linear canonical transform","volume":"60","author":"Chen","year":"2014","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_11","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. Lett."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"4013","DOI":"10.1109\/TSP.2016.2558161","article-title":"Long-time coherent integration for weak maneuvering target detection and high-order motion parameter estimation based on keystone transform","volume":"64","author":"Huang","year":"2016","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1016\/j.sigpro.2017.05.013","article-title":"Detection of weak maneuvering target based on keystone transformand matched filtering process","volume":"140","author":"Sun","year":"2017","journal-title":"Signal Process."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Li, Y., Zeng, T., Long, T., and Wang, Z. (2006, January 16\u201319). Range migration compensation and Doppler ambiguity resolution by keystone transform. Proceedings of the 2006 CIE International Conference on Radar (CIE ICR), Shanghai, China.","DOI":"10.1109\/ICR.2006.343404"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Li, S., Wang, Y., Wang, B., Battistelli, G., Chisci, L., and Cui, G. (2024). Efficient dual-scale generalized Radon-Fourier transform detector family for long time coherent integration. arXiv.","DOI":"10.1109\/TSP.2024.3411161"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"320","DOI":"10.1109\/TGRS.2016.2606436","article-title":"Ground maneuvering target imaging and high-order motion parameter estimation based on second-order keystone and generalized Hough-HAF transform","volume":"55","author":"Huang","year":"2017","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"270","DOI":"10.1109\/LSP.2014.2358230","article-title":"A fast maneuvering target motion parameters estimation algorithm based on ACCF","volume":"22","author":"Li","year":"2015","journal-title":"IEEE Signal Process Lett."},{"key":"ref_18","first-page":"4984","article-title":"High maneuvering target long-time coherent integration and motion parameters estimation based on Bayesian compressive sensing","volume":"59","author":"Yu","year":"2023","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Wang, B., Li, S., Battistelli, G., and Chisci, L. (2022, January 21\u201324). Dual-scale generalized Radon-Fourier transform family for long time coherent integration. Proceedings of the 11th International Conference on Control, Automation and Information Sciences (ICCAIS), Hanoi, Vietnam.","DOI":"10.1109\/ICCAIS56082.2022.9990039"},{"key":"ref_20","first-page":"146","article-title":"A method of designing signals of large time-bandwidth product","volume":"4","author":"Key","year":"1961","journal-title":"IRE Int. Conv. Rec."},{"key":"ref_21","unstructured":"Smith, J.O. (2024, March 12). Spectral Audio Signal Processing. Available online: http:\/\/books.w3k.org\/."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1980","DOI":"10.1109\/LWC.2022.3190423","article-title":"Fast iterative adaptive approach for indoor localization with distributed 5G small cells","volume":"11","author":"Wang","year":"2022","journal-title":"IEEE Wirel. Commun. Lett."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"560","DOI":"10.1109\/TSP.2002.807005","article-title":"Nonuniform fast Fourier transforms using minmax interpolation","volume":"51","author":"Fessler","year":"2003","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_24","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."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Lv, Y., Wu, Y., Wang, H., Qiu, L., Jiang, J., and Sun, Y. (2018). An inverse synthetic aperture ladar imaging algorithm of maneuvering target based on integral cubic phase function-fractional Fourier transform. Electronics, 7.","DOI":"10.3390\/electronics7080148"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"654","DOI":"10.1016\/j.dsp.2006.09.002","article-title":"Multicomponent chirp signals analysis using product cubic phase function","volume":"16","author":"Wang","year":"2006","journal-title":"Digit. Signal Process."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"456","DOI":"10.1049\/el.2017.3748","article-title":"Parameter estimation of CFM signals based on MICPF-HAF","volume":"54","author":"Zhang","year":"2018","journal-title":"Electron. Lett."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"6554","DOI":"10.1109\/TSP.2014.2364014","article-title":"Labeled Random finite sets and the Bayes multi-target tracking filter","volume":"62","author":"Vo","year":"2014","journal-title":"IEEE Trans. Signal Process."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/16\/10\/1798\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:44:37Z","timestamp":1760107477000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/16\/10\/1798"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,5,18]]},"references-count":28,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2024,5]]}},"alternative-id":["rs16101798"],"URL":"https:\/\/doi.org\/10.3390\/rs16101798","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2024,5,18]]}}}