{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:16:44Z","timestamp":1760145404551,"version":"build-2065373602"},"reference-count":23,"publisher":"MDPI AG","issue":"14","license":[{"start":{"date-parts":[[2024,7,22]],"date-time":"2024-07-22T00:00:00Z","timestamp":1721606400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key R&amp;D Program of China","award":["2018YFA0701903"],"award-info":[{"award-number":["2018YFA0701903"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>In recent years, with the miniaturization of high-precision position and orientation systems (POS), precise motion errors during SAR data collection can be calculated based on high-precision POS. However, compensating for these errors remains a significant challenge for multi-rotor UAV-borne SAR systems. Compared with large aircrafts, multi-rotor UAVs are lighter, slower, have more complex flight trajectories, and have larger squint angles, which result in significant differences in motion errors between building targets and ground targets. If the motion compensation is based on ground elevation, the motion error of the ground target will be fully compensated, but the building target will still have a large residual error; as a result, although the ground targets can be well-focused, the building targets may be severely defocused. Therefore, it is necessary to further compensate for the residual motion error of building targets based on the actual elevation on the SAR image. However, uncompensated errors will affect the time\u2013frequency relationship; furthermore, the \u03c9-k algorithm will further change these errors, resulting in errors in SAR images becoming even more complex and difficult to compensate for. To solve this problem, this paper proposes a novel improved precise topography and aperture-dependent (PTA) method that can precisely compensate for motion errors in the UAV-borne SAR system. After motion compensation and imaging processing based on ground elevation, a secondary focus is applied to defocused buildings. The improved PTA fully considers the coupling of the residual error with the time\u2013frequency relationship and \u03c9-k algorithm, and the precise errors in the two-dimensional frequency domain are determined through numerical calculations without any approximations. Simulation and actual data processing verify the effectiveness of the method, and the experimental results show that the proposed method in this paper is better than the traditional method.<\/jats:p>","DOI":"10.3390\/rs16142678","type":"journal-article","created":{"date-parts":[[2024,7,22]],"date-time":"2024-07-22T12:20:38Z","timestamp":1721650838000},"page":"2678","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Precise Motion Compensation of Multi-Rotor UAV-Borne SAR Based on Improved PTA"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5880-9684","authenticated-orcid":false,"given":"Yao","family":"Cheng","sequence":"first","affiliation":[{"name":"Suzhou Key Laboratory of Microwave Imaging, Processing and Application Technology, Suzhou 215124, China"},{"name":"National Key Laboratory of Microwave Imaging (Suzhou Branch), Suzhou 215124, China"},{"name":"Suzhou Aerospace Information Research Institute, Suzhou 215124, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8517-3415","authenticated-orcid":false,"given":"Xiaolan","family":"Qiu","sequence":"additional","affiliation":[{"name":"Suzhou Key Laboratory of Microwave Imaging, Processing and Application Technology, Suzhou 215124, China"},{"name":"National Key Laboratory of Microwave Imaging (Suzhou Branch), Suzhou 215124, China"},{"name":"Suzhou Aerospace Information Research Institute, Suzhou 215124, China"},{"name":"National Key Laboratory of Microwave Imaging Technology, Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100190, China"},{"name":"Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100094, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2931-6263","authenticated-orcid":false,"given":"Dadi","family":"Meng","sequence":"additional","affiliation":[{"name":"Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100094, China"},{"name":"Key Laboratory of Technology in Geo-Spatial Information Processing and Application Systems, Chinese Academy of Sciences, Beijing 100190, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,7,22]]},"reference":[{"key":"ref_1","unstructured":"Curlander, J., and McDonough, R. (1991). Synthetic Aperture Radar: Systems and Signal Processing, Wiley."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1109\/MGRS.2021.3113982","article-title":"Motion Compensation\/Autofocus in Airborne Synthetic Aperture Radar: A Review","volume":"10","author":"Chen","year":"2022","journal-title":"IEEE Geosci. Remote Sens. Mag."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"5458","DOI":"10.1109\/TGRS.2018.2817507","article-title":"Knowledge-Aided 2-D Autofocus for Spotlight SAR Range Migration Algorithm Imagery","volume":"56","author":"Mao","year":"2018","journal-title":"IEEE Trans. Geosci. Remote Sensing."},{"key":"ref_4","first-page":"1","article-title":"A Novel Autofocus Framework for UAV SAR Imagery: Motion Error Extraction from Symmetric Triangular FMCW Differential Signal","volume":"60","author":"Xu","year":"2022","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_5","first-page":"1","article-title":"Image Defocus in an Airborne UWB VHR Microwave Photonic SAR: Analysis and Compensation","volume":"60","author":"Xu","year":"2022","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1574","DOI":"10.1109\/JSEN.2011.2175216","article-title":"Wavenumber-Domain Autofocusing for Highly Squinted UAV SAR Imagery","volume":"12","author":"Zhang","year":"2012","journal-title":"IEEE Sens. J."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1580","DOI":"10.1109\/LGRS.2018.2848596","article-title":"A Motion Compensation Strategy for Airborne Repeat-Pass SAR Data","volume":"15","author":"Brancato","year":"2018","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_8","first-page":"764","article-title":"A New Approach to Airborne High-Resolution SAR Motion Compensation for Large Trajectory Deviations","volume":"21","author":"Meng","year":"2012","journal-title":"Chin. J. Electron."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2090","DOI":"10.1109\/JSTARS.2018.2799601","article-title":"Efficient Space-Variant Motion Compensation Approach for Ultra-High-Resolution SAR Based on Subswath Processing","volume":"11","author":"Yang","year":"2018","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1338","DOI":"10.1109\/TAES.2005.1561888","article-title":"Motion compensation errors: Effects on the accuracy of airborne SAR images","volume":"41","author":"Fornaro","year":"2005","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"826","DOI":"10.1109\/LGRS.2016.2548240","article-title":"An Inverse Extended Omega-K Algorithm for SAR Raw Data Simulation With Trajectory Deviations","volume":"13","author":"Huai","year":"2016","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Zheng, X., Yu, W., and Li, Z. (August, January 31). A Novel Algorithm for Wide Beam SAR Motion Compensation Based on Frequency Division. Proceedings of the 2006 IEEE International Symposium on Geoscience and Remote Sensing, Denver, CO, USA.","DOI":"10.1109\/IGARSS.2006.811"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1109\/LGRS.2007.895712","article-title":"Comparison of Topography- and Aperture-Dependent Motion Compensation Algorithms for Airborne SAR","volume":"4","author":"Prats","year":"2007","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"206","DOI":"10.1109\/LGRS.2005.846005","article-title":"Topography-Dependent Motion Compensation for Repeat-Pass Interferometric SAR Systems","volume":"2","author":"Prats","year":"2005","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"172","DOI":"10.1109\/LGRS.2004.842465","article-title":"Precise Topography- and Aperture-Dependent Motion Compensation for Airborne SAR","volume":"2","author":"Scheiber","year":"2005","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"204","DOI":"10.1049\/iet-rsn.2016.0195","article-title":"Precise Aperture-dependent Motion Compensation for High-resolution Synthetic Aperture Radar Imaging","volume":"11","author":"Wang","year":"2017","journal-title":"IET Radar Sonar Navig."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1493","DOI":"10.1109\/LGRS.2013.2260721","article-title":"Azimuth-to-Frequency Mapping in Airborne SAR Data Corrupted by Uncompensated Motion Errors","volume":"10","author":"Perna","year":"2013","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Lu, Q., Du, K., and Li, Q. (2021, January 3\u20135). Improved Precise Tomography- and Aperture-Dependent Compensation for Synthetic Aperture Radar. Proceedings of the 2021 2nd China International SAR Symposium (CISS), Shanghai, China.","DOI":"10.23919\/CISS51089.2021.9652353"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2510","DOI":"10.1109\/TGRS.2014.2361134","article-title":"Precise Focusing of Airborne SAR Data With Wide Apertures Large Trajectory Deviations: A Chirp Modulated Back-Projection Approach","volume":"53","author":"Meng","year":"2015","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1109\/TGRS.2017.2744649","article-title":"On the Processing of Very High Resolution Spaceborne SAR Data: A Chirp-Modulated Back Projection Approach","volume":"56","author":"Meng","year":"2018","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1460","DOI":"10.1109\/LGRS.2013.2295326","article-title":"A Fast BP Algorithm With Wavenumber Spectrum Fusion for High-Resolution Spotlight SAR Imaging","volume":"11","author":"Zhang","year":"2014","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1219","DOI":"10.1109\/LGRS.2012.2236817","article-title":"Improvements to the Frequency Division-Based Subaperture Algorithm for Motion Compensation in Wide-Beam SAR","volume":"10","author":"Li","year":"2013","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"2221","DOI":"10.1109\/JSTARS.2023.3245827","article-title":"Analysis and Compensation for Systematical Errors in Airborne Microwave Photonic SAR Imaging by 2-D Autofocus","volume":"16","author":"Chen","year":"2023","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\/16\/14\/2678\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T15:21:06Z","timestamp":1760109666000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/16\/14\/2678"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,7,22]]},"references-count":23,"journal-issue":{"issue":"14","published-online":{"date-parts":[[2024,7]]}},"alternative-id":["rs16142678"],"URL":"https:\/\/doi.org\/10.3390\/rs16142678","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2024,7,22]]}}}