{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,14]],"date-time":"2026-03-14T18:29:34Z","timestamp":1773512974464,"version":"3.50.1"},"reference-count":35,"publisher":"MDPI AG","issue":"19","license":[{"start":{"date-parts":[[2024,9,28]],"date-time":"2024-09-28T00:00:00Z","timestamp":1727481600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["61971224"],"award-info":[{"award-number":["61971224"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>In inverse synthetic aperture radar (ISAR) systems, image quality often suffers from the non-uniform rotation of non-cooperative targets. Rotational motion compensation (RMC) is necessary to perform refocused ISAR imaging via estimated rotational motion parameters. However, estimation errors tend to accumulate with the estimated processes, deteriorating the image quality. A novel RMC algorithm is proposed in this study to mitigate the impact of cumulative errors. The proposed method uses an iterative approach based on a novel criterion, i.e., the minimum residual norm of the signal phases, to estimate different rotational parameters independently to avoid the issue caused by cumulative errors. First, a refined inverse function combined with interpolation is proposed to perform the RMC procedure. Then, the rotation parameters are estimated using an iterative procedure designed to minimize the residual norm of the compensated signal phases. Finally, with the estimated parameters, RMC is performed on signals in all range bins, and focused images are obtained using the Fourier transform. Furthermore, this study utilizes simulated and real data to validate and evaluate the performance of the proposed algorithm. The experimental results demonstrate that the proposed algorithm shows dominance in the aspects of estimation accuracy, entropy values, and focusing characteristics.<\/jats:p>","DOI":"10.3390\/rs16193629","type":"journal-article","created":{"date-parts":[[2024,9,30]],"date-time":"2024-09-30T05:45:27Z","timestamp":1727675127000},"page":"3629","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Rotational Motion Compensation for ISAR Imaging Based on Minimizing the Residual Norm"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0009-0000-7502-7089","authenticated-orcid":false,"given":"Xiaoyu","family":"Yang","sequence":"first","affiliation":[{"name":"School of Electronic and Optical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7262-9607","authenticated-orcid":false,"given":"Weixing","family":"Sheng","sequence":"additional","affiliation":[{"name":"School of Electronic and Optical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-1934-6453","authenticated-orcid":false,"given":"Annan","family":"Xie","sequence":"additional","affiliation":[{"name":"School of Electronic and Optical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China"}]},{"given":"Renli","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Electronic and Optical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,9,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1109\/TAES.1980.308875","article-title":"Range-Doppler Imaging of Rotating Objects","volume":"AES\u201316","author":"Walker","year":"1980","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_2","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_3","doi-asserted-by":"crossref","first-page":"1056","DOI":"10.1109\/7.953256","article-title":"Robust autofocus algorithm for ISAR imaging of moving targets","volume":"37","author":"Li","year":"2001","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1418","DOI":"10.1109\/TGRS.2013.2251348","article-title":"ISAR imaging of a ship target based on parameter estimation of multicomponent quadratic frequency-modulated signals","volume":"52","author":"Bai","year":"2014","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_5","first-page":"3364","article-title":"Comparison of various Algorithms for RD, RID and RIC methods using ISAR imaging","volume":"11","author":"Guttavelli","year":"2016","journal-title":"Int. J. Appl. Eng. Res."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"204","DOI":"10.1109\/LGRS.2008.2010562","article-title":"Robust ISAR range alignment via minimizing the entropy of the average range profile","volume":"6","author":"Zhu","year":"2009","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2950","DOI":"10.1109\/TAES.2016.150883","article-title":"Efficient ISAR autofocus via minimization of Tsallis Entropy","volume":"52","author":"Kang","year":"2016","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Xia, S., Wang, Y., Zhang, J., and Dai, F. (2023). High-Speed Maneuvering Target Inverse Synthetic Aperture Radar Imaging and Motion Parameter Estimation Based on Fast Spare Bayesian Learning and Minimum Entropy. Remote Sens., 15.","DOI":"10.3390\/rs15133376"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Liu, C., Luo, Y., Yu, Z., and Feng, J. (2023). ISAR Imaging of Non-Stationary Moving Target Based on Parameter Estimation and Sparse Decomposition. Remote Sens., 15.","DOI":"10.3390\/rs15092368"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Wang, Z., Yang, W., Chen, Z., Zhao, Z., Hu, H., and Qi, C. (2018). A Novel Adaptive Joint Time Frequency Algorithm by the Neural Network for the ISAR Rotational Compensation. Remote Sens., 10.","DOI":"10.3390\/rs10020334"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Li, W., Yuan, Y., Zhang, Y., and Luo, Y. (2022). Unblurring ISAR Imaging for Maneuvering Target Based on UFGAN. Remote Sens., 14.","DOI":"10.3390\/rs14205270"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Shi, H., Yang, T., and Qiao, Z. (2018). ISAR Autofocus Imaging Algorithm for Maneuvering Targets Based on Phase Retrieval and Gabor Wavelet Transform. Remote Sens., 10.","DOI":"10.3390\/rs10111810"},{"key":"ref_13","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_14","doi-asserted-by":"crossref","first-page":"921","DOI":"10.1049\/iet-rsn.2012.0091","article-title":"Inverse synthetic aperture radar imaging of manoeuvring target based on range-instantaneous-Doppler and range-instantaneous-chirp-rate algorithms","volume":"6","author":"Wang","year":"2012","journal-title":"IET Radar Sonar Navig."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"7010","DOI":"10.1109\/JSEN.2020.2977665","article-title":"Rotation parameters estimation and cross-range scaling research for range instantaneous doppler ISAR images","volume":"20","author":"Wang","year":"2020","journal-title":"IEEE Sens. J."},{"key":"ref_16","first-page":"5944","article-title":"Efficient ISAR imaging approach for nonuniformly rotating targets based on ICPF-PPP","volume":"58","author":"Kang","year":"2022","journal-title":"IEEE Trans. Image Process."},{"key":"ref_17","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_18","first-page":"1","article-title":"ISAR imaging of a maneuvering target based on parameter estimation of multicomponent cubic phase signals","volume":"660","author":"Huang","year":"2022","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1119","DOI":"10.1109\/TAES.2017.2667538","article-title":"ISAR imaging of nonuniformly rotating target based on the multicomponent CPS model under low SNR environment","volume":"53","author":"Li","year":"2017","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"3108","DOI":"10.1109\/TAES.2018.2845138","article-title":"An ISAR imaging algorithm for nonuniformly rotating targets with low SNR based on modified bilinear parameter estimation of cubic phase signal","volume":"54","author":"Lv","year":"2018","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"74707","DOI":"10.1109\/ACCESS.2020.2985533","article-title":"ISAR imaging of nonuniformly rotating targets with low SNR based on third order autocorrelation function","volume":"8","author":"Li","year":"2020","journal-title":"IEEE Access"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1074","DOI":"10.1109\/LGRS.2020.2992513","article-title":"ISAR imaging of nonuniformly rotating targets with low SNR based on coherently integrated nonuniform trilinear autocorrelation function","volume":"18","author":"Li","year":"2021","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Wu, W., Xu, S., Hu, P., Zou, J., and Chen, Z. (2018). Inverse Synthetic Aperture Radar Imaging of Targets with Complex Motion based on Optimized Non-Uniform Rotation Transform. Remote Sens., 10.","DOI":"10.3390\/rs10040593"},{"key":"ref_24","first-page":"382","article-title":"Inverse synthetic aperture radar image focusing using fast adaptive joint time-frequency and three-dimensional motion detection on experimental radar data","volume":"4","author":"Thayaparan","year":"2010","journal-title":"IET Radar Sonar Navig."},{"key":"ref_25","first-page":"329","article-title":"Focusing inverse synthetic aperture radar images with higher-order motion error using the adaptive joint-time frequency algorithm optimized with the genetic algorithm and the particle swarm optimization algorithm comparison and results","volume":"3","author":"Brinkman","year":"2009","journal-title":"IET Signal Process."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1049\/iet-rsn.2013.0392","article-title":"Cross-range scaling method of inverse synthetic aperture radar image based on discrete polynomial-phase transform","volume":"9","author":"Liu","year":"2015","journal-title":"IET Radar Sonar Navig."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1551","DOI":"10.1002\/mop.29849","article-title":"Isar rotational motion compensation algorithm using polynomial phase transform","volume":"58","author":"Kang","year":"2016","journal-title":"Microw. Opt. Technol. Lett."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Ozdemir, C. (2021). Inverse Synthetic Aperture Radar with MATLAB Algorithms, John Wiley and Sons. [2nd ed.].","DOI":"10.1002\/9781119521396"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1109\/TAES.2005.1468738","article-title":"Estimation and classification of FM signals using time frequency transforms","volume":"41","author":"Jauffret","year":"2005","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1901","DOI":"10.1109\/78.403349","article-title":"The discrete polynomial-phase transform","volume":"43","author":"Peleg","year":"1995","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"963","DOI":"10.1109\/TAES.2010.5545167","article-title":"Integrated Cubic Phase Function for Linear FM Signal Analysis","volume":"46","author":"Wang","year":"2010","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"5677","DOI":"10.1109\/TIE.2015.2415756","article-title":"Frequency and Phase-Angle Estimation Using Ordinary Least Squares","volume":"62","author":"Ramos","year":"2015","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"4554","DOI":"10.1109\/TGRS.2015.2401602","article-title":"RPC Estimation via \u21131-Norm-Regularized Least Squares (L1LS)","volume":"53","author":"Long","year":"2015","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"64324","DOI":"10.1109\/ACCESS.2020.2984487","article-title":"ISAR imaging of non-uniform rotating targets based on optimized matching Fourier transform","volume":"8","author":"Zuo","year":"2020","journal-title":"IEEE Access"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"537","DOI":"10.1051\/jnwpu\/20234130537","article-title":"Target recognition algorithm based on HRRP time-spectrogram feature and multi-scale asymmetric convolutional neural network","volume":"43","author":"Yun","year":"2023","journal-title":"J. Northwest. Polytech. Univ."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/16\/19\/3629\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T16:06:16Z","timestamp":1760112376000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/16\/19\/3629"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,9,28]]},"references-count":35,"journal-issue":{"issue":"19","published-online":{"date-parts":[[2024,10]]}},"alternative-id":["rs16193629"],"URL":"https:\/\/doi.org\/10.3390\/rs16193629","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,9,28]]}}}