{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,9]],"date-time":"2026-07-09T13:15:01Z","timestamp":1783602901383,"version":"3.55.0"},"reference-count":27,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2026,7,8]],"date-time":"2026-07-08T00:00:00Z","timestamp":1783468800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Imaging"],"abstract":"<jats:p>Geosynchronous spaceborne\u2013airborne frequency-modulated continuous-wave bistatic synthetic aperture radar (GEO SA FMCW BiSAR) offers cost-effective and persistent target monitoring. However, both the maneuvers of the receiver during the signal propagation delay and the continuous movements of the radar platforms within the sweep complicate the received echo signal. These factors invalidate the \u201cstop-and-go\u201d assumption, which presumes constant-velocity motion. This paper proposes an echo model that simultaneously considers intra-pulse motion and accelerated motion of the high-maneuvering receiver. The introduction of receiver acceleration leads to nonlinear range terms in the bistatic range history, which will degrade the focusing performance if not properly compensated. Since the acceleration term is a small second-order quantity relative to the time delay, it is approximated by segmenting the aperture and applying the \u201cstop-and-go\u201d assumption within each sub-aperture. After dechirp, the two-dimensional (2-D) spectrum for imaging is derived by applying the principle of stationary phase and determining the azimuth stationary phase point via series reversion. Finally, imaging is achieved by azimuth compression, range cell migration correction, and secondary range compression. Simulation results demonstrate that the proposed algorithm achieves well-focused images while maintaining computational efficiency.<\/jats:p>","DOI":"10.3390\/jimaging12070310","type":"journal-article","created":{"date-parts":[[2026,7,8]],"date-time":"2026-07-08T16:16:18Z","timestamp":1783527378000},"page":"310","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Echo Model Analysis and Frequency-Domain Imaging Algorithm for Geosynchronous Spaceborne\u2013Airborne FMCW Bistatic SAR with High-Maneuvering Receiver"],"prefix":"10.3390","volume":"12","author":[{"given":"Xinyu","family":"Liu","sequence":"first","affiliation":[{"name":"School of Health Science and Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7438-3057","authenticated-orcid":false,"given":"Li","family":"Ding","sequence":"additional","affiliation":[{"name":"School of Health Science and Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chenlei","family":"Lu","sequence":"additional","affiliation":[{"name":"School of Optical-Electrical and Computer Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wenlong","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Optical-Electrical and Computer Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ping","family":"Li","sequence":"additional","affiliation":[{"name":"School of Optical-Electrical and Computer Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,7,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"3713","DOI":"10.1109\/TGRS.2018.2886817","article-title":"A Two-Step Nonlinear Chirp Scaling Method for Multichannel GEO Spaceborne\u2013Airborne Bistatic SAR Spectrum Reconstructing and Focusing","volume":"57","author":"An","year":"2019","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Zhang, Q., Dong, Z., Zhang, Y., and He, Z. (2016, January 10\u201315). GEO-UAV Bistatic Circular Synthetic Aperture Radar: Concepts and Technologies. Proceedings of the 2016 IEEE International Geoscience and Remote Sensing Symposium (IGARSS), Beijing, China.","DOI":"10.1109\/IGARSS.2016.7730093"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1109\/TGRS.2015.2457034","article-title":"Inclined Geosynchronous Spaceborne\u2013Airborne Bistatic SAR: Performance Analysis and Mission Design","volume":"54","author":"Sun","year":"2016","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"176291","DOI":"10.1109\/ACCESS.2019.2953767","article-title":"Spaceborne Azimuth Multichannel BiSAR with Geosynchronous Transmitter and LEO Receiver: High-Resolution Wide-Swath Image Formation","volume":"7","author":"Wang","year":"2019","journal-title":"IEEE Access"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Zhou, B., Qi, X., and Zhang, H. (2021). An Accurate GEO SAR Range Model for Ultralong Integration Time Based on mth-Order Taylor Expansion. Remote Sens., 13.","DOI":"10.3390\/rs13020255"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Hu, X., Xie, H., Yi, S., Zhang, L., and Lu, Z. (2024). An Improved NLCS Algorithm Based on Series Reversion and Elliptical Model Using Geosynchronous Spaceborne\u2013Airborne UHF UWB Bistatic SAR for Oceanic Scene Imaging. Remote Sens., 16.","DOI":"10.3390\/rs16071131"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Liu, L., Hou, Y., Chen, T., Sun, H., and Sun, Z. (2025, January 3\u20138). A Novel Imaging Algorithm for Spaceborne-Airborne Beam Steering Bistatic SAR. Proceedings of the IGARSS 2025\u20132025 IEEE International Geoscience and Remote Sensing Symposium, Brisbane, Australia.","DOI":"10.1109\/IGARSS55030.2025.11243412"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Cui, C., Dong, X., Hu, C., and Tian, W. (2021, January 11\u201316). An Adaptive Moving Target Indication Method for GEO Spaceborne-Airborne Bistatic SAR. Proceedings of the 2021 IEEE International Geoscience and Remote Sensing Symposium IGARSS, Brussels, Belgium.","DOI":"10.1109\/IGARSS47720.2021.9553214"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Cui, C., Dong, X., Chen, Z., Hu, C., and Tian, W. (2022). A Long-Time Coherent Integration STAP for GEO Spaceborne-Airborne Bistatic SAR. Remote Sens., 14.","DOI":"10.3390\/rs14030593"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Zhang, S., Zhang, S., Guo, T., Xu, R., Liu, Z., and Du, Q. (2025). Clutter Modeling and Characteristics Analysis for GEO Spaceborne\u2013Airborne Bistatic Radar. Remote Sens., 17.","DOI":"10.3390\/rs17071222"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Li, J., Li, C., Tan, X., You, D., Duan, C., Zhang, S., Dang, H., Li, G., and Zhang, Q. (2025). A Review of Recent Development of Geosynchronous Synthetic Aperture Radar Technique. Remote Sens., 17.","DOI":"10.3390\/rs17203405"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Wang, H., Chen, X., Zheng, S., Yang, D., and Wu, S. (2021, January 3\u20135). Analysis of Spatial Synchronization Errors for Spaceborne Bistatic SAR System. Proceedings of the 2021 2nd China International SAR Symposium (CISS), Shanghai, China.","DOI":"10.23919\/CISS51089.2021.9652368"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Liu, Y., Wei, Y., Qiu, J., Song, J., Xu, K., Zhao, F., Chen, Z., Feng, X., Zhao, H., and Zhang, M. (2026). A Novel Lightweight and Compact Multi-Rotor UAV Ka-Band Pulse-Doppler Synthetic Aperture Radar System. Remote Sens., 18.","DOI":"10.3390\/rs18071047"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1109\/83.128031","article-title":"A System Model and Inversion for Synthetic Aperture Radar Imaging","volume":"1","author":"Soumekh","year":"1992","journal-title":"IEEE Trans. Image Process."},{"key":"ref_15","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_16","unstructured":"Meta, A., Hoogeboom, P., and Ligthart, L.P. (2006, January 24\u201327). Correction of the Effects Induced by the Continuous Motion in Airborne FMCW SAR. Proceedings of the 2006 IEEE Conference on Radar, Verona, NY, USA."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"3548","DOI":"10.1109\/TGRS.2011.2160402","article-title":"The Accurate Focusing and Resolution Analysis Method in Geosynchronous SAR","volume":"49","author":"Hu","year":"2011","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_18","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":"Liu","year":"2012","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_19","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_20","doi-asserted-by":"crossref","first-page":"348","DOI":"10.1109\/TGRS.2020.2992744","article-title":"Nonambiguous Image Formation for Low-Earth-Orbit SAR with Geosynchronous Illumination Based on Multireceiving and CAMP","volume":"59","author":"An","year":"2021","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"An, H., Lv, Z., Pu, X., Sun, Z., Wu, J., Li, Z., and Yang, J. (2022, January 17\u201322). An Accurate Range Model for Geo Spaceborne-Airborne Bistatic Sar. Proceedings of the IGARSS 2022\u20132022 IEEE International Geoscience and Remote Sensing Symposium, Kuala Lumpur, Malaysia.","DOI":"10.1109\/IGARSS46834.2022.9883278"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Zhang, Y., and Fang, L. (2019, January 12\u201314). Imaging for Bistatic Airborne Frequency Modulated Continuous Wave SAR. Proceedings of the 2019 International Conference on Electronic Engineering and Informatics (EEI), Nanjing, China.","DOI":"10.1109\/EEI48997.2019.00042"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"3519","DOI":"10.1109\/TGRS.2007.906140","article-title":"Signal Processing for FMCW SAR","volume":"45","author":"Meta","year":"2007","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Feng, L., Wang, H., Zheng, S., Zhao, Q., Zeng, Z., and Chen, X. (2021, January 3\u20135). Spaceborne Bistatic FMCW SAR Imaging Method Based on FS Algorithm. Proceedings of the 2021 2nd China International SAR Symposium (CISS), Shanghai, China.","DOI":"10.23919\/CISS51089.2021.9652211"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Zhang, F., Luo, C., Fu, Y., Zhang, W., Yang, W., Yu, R., and Yan, S. (2023). Frequency Domain Imaging Algorithms for Short-Range Synthetic Aperture Radar. Remote Sens., 15.","DOI":"10.3390\/rs15245684"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"32123","DOI":"10.3390\/s151229910","article-title":"Focusing Bistatic FMCW SAR Signal by Range Migration Algorithm Based on Fresnel Approximation","volume":"15","author":"Li","year":"2015","journal-title":"Sensors"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"5205615","DOI":"10.1109\/TGRS.2026.3672786","article-title":"An Extended Ground Cartesian Back-Projection Imaging Algorithm for High-Resolution Spaceborne Bistatic FMCW-SAR","volume":"64","author":"Zeng","year":"2026","journal-title":"IEEE Trans. Geosci. Remote Sens."}],"container-title":["Journal of Imaging"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2313-433X\/12\/7\/310\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,7,9]],"date-time":"2026-07-09T12:29:51Z","timestamp":1783600191000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2313-433X\/12\/7\/310"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,7,8]]},"references-count":27,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2026,7]]}},"alternative-id":["jimaging12070310"],"URL":"https:\/\/doi.org\/10.3390\/jimaging12070310","relation":{},"ISSN":["2313-433X"],"issn-type":[{"value":"2313-433X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,7,8]]}}}