{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,14]],"date-time":"2025-10-14T00:47:06Z","timestamp":1760402826039,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2021,4,10]],"date-time":"2021-04-10T00:00:00Z","timestamp":1618012800000},"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":["61201284, 61801204 and 62061031"],"award-info":[{"award-number":["61201284, 61801204 and 62061031"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Shaanxi Innovative Talents Promotion Plan-Science and Technology Innovation Team","award":["2019TD-002"],"award-info":[{"award-number":["2019TD-002"]}]},{"name":"public foundation from Key Laboratory of EMW Information , Fudan University, China","award":["EMW201901"],"award-info":[{"award-number":["EMW201901"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Due to the independence of azimuth-invariant assumption of an echo signal, time-domain algorithms have significant performance advantages for missile-borne synthetic aperture radar (SAR) focusing with curve moving trajectory. The Cartesian factorized back projection (CFBP) algorithm is a newly proposed fast time-domain implementation which can avoid massive interpolations to improve the computational efficiency. However, it is difficult to combine effective and efficient data-driven motion compensation (MOCO) for achieving high focusing performance. In this paper, a new data-driven MOCO algorithm is developed under the CFBP framework to deal with the motion error problem for missile-borne SAR application. In the algorithm, spectrum compression is implemented after a CFBP process, and the SAR images are transformed into the spectrum-compressed domain. Then, the analytical image spectrum is obtained by utilizing wavenumber decomposition based on which the property of motion induced error is carefully investigated. With the analytical image spectrum, it is revealed that the echoes from different scattering points are aligned in the same spectrum range and the phase error becomes a spatial invariant component after spectrum compression. Based on the spectrum-compressed domain, an effective and efficient data-driven MOCO algorithm is accordingly developed for accurate error estimation and compensation. Both simulations of missile-borne SAR and raw data experiment from maneuvering highly-squint airborne SAR are provided and analyzed, which show high focusing performance of the proposed algorithm.<\/jats:p>","DOI":"10.3390\/rs13081462","type":"journal-article","created":{"date-parts":[[2021,4,12]],"date-time":"2021-04-12T05:52:00Z","timestamp":1618206720000},"page":"1462","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Processing Missile-Borne SAR Data by Using Cartesian Factorized Back Projection Algorithm Integrated with Data-Driven Motion Compensation"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4625-5872","authenticated-orcid":false,"given":"Min","family":"Bao","sequence":"first","affiliation":[{"name":"School of Electronic Engineering, Xidian University, Xi\u2019an 710071, China"}]},{"given":"Song","family":"Zhou","sequence":"additional","affiliation":[{"name":"School of Electronic Information and Engineering, Nanchang University, Nanchang 330031, China"}]},{"given":"Mengdao","family":"Xing","sequence":"additional","affiliation":[{"name":"National Laboratory of Radar Signal Processing, Xidian University, Xi\u2019an 710071, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,4,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"3546","DOI":"10.1109\/JSTARS.2021.3062286","article-title":"TanDEM-X: 10 Years of Formation Flying Bistatic SAR Interferometry","volume":"14","author":"Zink","year":"2021","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Wan, J., Tan, X., Chen, Z., Dong, L., Liu, Q., Zhou, Y., and Zhang, L. (2021). Refocusing of Ground Moving Targets with Doppler Ambiguity Using Keystone Transform and Modified Second-Order Keystone Transform for Synthetic Aperture Radar. Remote Sens., 2.","DOI":"10.3390\/rs13020177"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"111255","DOI":"10.1016\/j.rse.2019.111255","article-title":"The legacy of the SIR-C\/X-SAR radar system: 25 years on","volume":"231","author":"Freeman","year":"2019","journal-title":"Remote Sens. Environ."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Luebeck, D., Wimmer, C., Moreira, L.F., Alc\u00e2ntara, M., Or\u00e9, G., G\u00f3es, J.A., Oliveira, L.P., Teruel, B., Bins, L.S., and Gabrielli, L.H. (2020). Drone-borne differential SAR interferometry. Sensors, 12.","DOI":"10.3390\/rs12050778"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"6974","DOI":"10.1109\/TGRS.2019.2909729","article-title":"High-speed maneuvering platforms squint beam-steering SAR imaging without subaperture","volume":"57","author":"Bie","year":"2019","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_6","first-page":"016502","article-title":"Maneuvering platform high-squint SAR imaging method based on perturbation KT and subregion phase filtering","volume":"1","author":"Li","year":"2021","journal-title":"J. Appl. Remote Sens."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2724","DOI":"10.1109\/TAES.2018.2828238","article-title":"An extended fast factorized back projection algorithm for missile-borne bistatic forward-looking SAR imaging","volume":"54","author":"Feng","year":"2018","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Tang, S., Guo, P., Zhang, L., and Lin, C. (2019). Modeling and Precise Processing for Spaceborne Transmitter\/Missile-Borne Receiver SAR Signals. Remote Sens., 11.","DOI":"10.3390\/rs11030346"},{"key":"ref_9","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., 16.","DOI":"10.3390\/rs12162616"},{"key":"ref_10","unstructured":"Cumming, I.G., and Wong, F.H. (2004). Digital Signal Processing of Synthetic Aperture Radar Data: Algorithms and Implementation, Artech House."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"6390","DOI":"10.1109\/TGRS.2017.2727060","article-title":"A 2D space-variant motion estimation and compensation method for ultrahigh-resolution airborne stepped-frequency SAR with long integration time","volume":"55","author":"Chen","year":"2017","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_12","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_13","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1109\/83.199920","article-title":"Convolution backprojection image reconstruction for spotlight mode synthetic aperture radar","volume":"1","author":"Desai","year":"1992","journal-title":"IEEE Trans. Image Process."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Zhang, Y., Zhang, Q., Zhang, Y., Pei, J., Huang, Y., and Yang, J. (2020). Fast split bregman based deconvolution algorithm for airborne radar imaging. Remote Sens., 12.","DOI":"10.3390\/rs12111747"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Gaibel, A., and Boag, A. (2020). Backprojection Imaging of Moving Objects. IEEE Trans. Image Process.","DOI":"10.1109\/TAP.2020.3045500"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Lin, C., Tang, S., Zhang, L., and Guo, P. (2018). Focusing High-Resolution Airborne SAR with Topography Variations Using an Extended BPA Based on a Time\/Frequency Rotation Principle. Remote Sens., 8.","DOI":"10.3390\/rs10081275"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1394","DOI":"10.1109\/LGRS.2013.2258886","article-title":"Integrating autofocus techniques with fast factorized back-projection for high-resolution spotlight SAR imaging","volume":"10","author":"Zhang","year":"2013","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"9041","DOI":"10.1109\/TGRS.2019.2924221","article-title":"Knowledge-Aided 2D Autofocus for Spotlight SAR Filtered Backprojection Imagery","volume":"57","author":"Mao","year":"2019","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_19","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_20","first-page":"96","article-title":"SAS image reconstruction using fast polar back projection: Comparisons with fast factored back projection and Fourier-domain imaging","volume":"1","author":"Shippey","year":"2005","journal-title":"Eur. Ocean."},{"key":"ref_21","unstructured":"Yang, Z., Sun, G.-C., and Xing, M. (2013, January 23\u201327). A new fast back-projection algorithm using polar format algorithm. Proceedings of the 2013 Asia-Pacific Conference on Synthetic Aperture Radar (APSAR), Tsukuba, Japan."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1109\/TSP.2014.2375157","article-title":"Nyquist sampling requirements for polar grids in bistatic time-domain algorithms","volume":"63","author":"Vu","year":"2014","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_23","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 Obs. Remote Sens."},{"key":"ref_24","first-page":"1160","article-title":"Cartesian factorized backprojection algorithm for high-resolution spotlight SAR imaging","volume":"3","author":"Dong","year":"2017","journal-title":"IEEE Sens. J."},{"key":"ref_25","first-page":"902","article-title":"A modified cartesian factorized back-projection algorithm for highly squint spotlight synthetic aperture radar imaging","volume":"6","author":"Luo","year":"2018","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_26","doi-asserted-by":"crossref","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.","DOI":"10.1109\/TGRS.2020.3011589"},{"key":"ref_27","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":"8","author":"Luo","year":"2018","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"2870","DOI":"10.1109\/TGRS.2009.2015657","article-title":"Motion compensation for UAV SAR based on raw radar data","volume":"8","author":"Xing","year":"2009","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"3202","DOI":"10.1109\/TGRS.2011.2180392","article-title":"A robust motion compensation approach for UAV SAR imagery","volume":"8","author":"Zhang","year":"2012","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"2232","DOI":"10.1109\/TIP.2021.3051484","article-title":"Deep SAR Imaging and Motion Compensation","volume":"30","author":"Pu","year":"2021","journal-title":"IEEE Trans. Image Process."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"7053","DOI":"10.1109\/TGRS.2017.2739133","article-title":"Quasi-polar-based FFBP algorithm for miniature UAV SAR imaging without navigational data","volume":"55","author":"Zhou","year":"2017","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"3949","DOI":"10.1109\/JSTARS.2019.2945118","article-title":"Fast Factorized Backprojection Imaging Algorithm Integrated With Motion Trajectory Estimation for Bistatic Forward-Looking SAR","volume":"12","author":"Pu","year":"2019","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"5132","DOI":"10.1109\/TGRS.2020.2972972","article-title":"Cooperative Multitask Learning for Sparsity-Driven SAR Imagery and Nonsystematic Error Autocalibration","volume":"58","author":"Yang","year":"2020","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"827","DOI":"10.1109\/7.303752","article-title":"Phase gradient autofocus-a robust tool for high resolution SAR phase correction","volume":"3","author":"Wahl","year":"1994","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"2487","DOI":"10.1109\/36.789644","article-title":"Weighted least-squares estimation of phase errors for SAR\/ISAR autofocus","volume":"5","author":"Ye","year":"1999","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1728","DOI":"10.1109\/JSTARS.2020.3002394","article-title":"Data-driven Motion Compensation for Airborne Bistatic SAR Imagery under Fast Factorized Back Projection Framework","volume":"14","author":"Bao","year":"2021","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/8\/1462\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T13:59:18Z","timestamp":1760363958000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/8\/1462"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,4,10]]},"references-count":36,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2021,4]]}},"alternative-id":["rs13081462"],"URL":"https:\/\/doi.org\/10.3390\/rs13081462","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2021,4,10]]}}}