{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T05:56:38Z","timestamp":1761630998469,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"14","license":[{"start":{"date-parts":[[2022,7,16]],"date-time":"2022-07-16T00:00:00Z","timestamp":1657929600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["62131001","62171029"],"award-info":[{"award-number":["62131001","62171029"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Due to the short wavelength of the terahertz wave, airborne terahertz synthetic aperture radar (THz-SAR) suffers from echo phase errors caused by the high-frequency vibration of the platform. These errors will result in defocusing and the emergence of ghost targets, which will degrade the quality of the image. Therefore, it is necessary to compensate for phase errors in order to bring the image into focus. This paper proposes a multi-component high-frequency vibration parameter estimation method based on chirplet decomposition and least squares (LS) sequential estimators, which differs from other methods that can only be applied to simple harmonic vibrations. In particular, we first obtain the instantaneous chirp rate (ICR) of the signal by chirplet decomposition. Then, we employ the LS sequential estimators in conjunction with separable regression technique (SRT) to estimate vibration parameters. The estimated parameters are subsequently used to re-establish the ICR components for each vibration component and these parameters are further re-estimated to improve their accuracy. Based on the estimated parameters, phase compensation functions can be constructed to suppress the defocusing and ghost targets in airborne THz-SAR imaging. Simulated results on point targets and distributed imaging scenes demonstrate that the proposed method is accurate and reliable even at low signal-to-noise ratios (SNRs).<\/jats:p>","DOI":"10.3390\/rs14143416","type":"journal-article","created":{"date-parts":[[2022,7,18]],"date-time":"2022-07-18T01:53:22Z","timestamp":1658109202000},"page":"3416","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Estimation of High-Frequency Vibration Parameters for Airborne Terahertz SAR Using Chirplet Decomposition and LS Sequential Estimators"],"prefix":"10.3390","volume":"14","author":[{"given":"Zhaoxin","family":"Hao","sequence":"first","affiliation":[{"name":"School of Electronics and Information Engineering, Beihang University, Beijing 100191, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7184-5057","authenticated-orcid":false,"given":"Jinping","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Electronics and Information Engineering, Beihang University, Beijing 100191, China"}]},{"given":"Qing","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, UK"}]},{"given":"Tao","family":"Shan","sequence":"additional","affiliation":[{"name":"School of Information and Electronics, Beijing Institute of Technology, Beijing 100081, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,7,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"999","DOI":"10.1109\/TTHZ.2015.2474115","article-title":"THz Absorption in Fabric and Its Impact on Body Scanning for Security Application","volume":"5","author":"Knipper","year":"2015","journal-title":"IEEE Trans. Terahertz Sci. Technol."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Wang, Q., Zhou, H., Wang, Y., Xia, R., Liu, Q., Zhao, B., and Wang, Y. (2020, January 15\u201317). Super-Resolution Imaging Using Very Deep Convolutional Network in Terahertz NDT Field. Proceedings of the International Charter: Space and Major Disasters (ICSMD), Xi\u2019an, China.","DOI":"10.1109\/ICSMD50554.2020.9261696"},{"key":"ref_3","unstructured":"Ding, X., Xu, J., Chen, Q., Fu, C., and Ni, L. (2020, January 4\u20136). Retrieval of ice cloud properties with a dual frequency optimal estimation algorithm for terahertz and millimeter wave cloud radar. Proceedings of the IET International Radar Conference, Online Conference."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"897","DOI":"10.1109\/LGRS.2018.2886750","article-title":"Improved Method of Video Synthetic Aperture Radar Imaging Algorithm","volume":"16","author":"Zuo","year":"2019","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Kim, S., Fan, R., and Dominski, F. (2018, January 23\u201327). ViSAR: A 235 GHz radar for airborne applications. Proceedings of the 2018 IEEE Radar Conference, Oklahoma City, OK, USA.","DOI":"10.1109\/RADAR.2018.8378797"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"3762","DOI":"10.3390\/s22103762","article-title":"Object Recognition in High-Resolution Indoor THz SAR Mapped Environment","volume":"22","author":"Batra","year":"2022","journal-title":"Sensors"},{"key":"ref_7","unstructured":"Carrara, W.G., Goodman, R.S., and Majewski, R.M. (1995). Spotlight Synthetic Aperture Radar: Signal Processing Algorithms, Artech House."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2729","DOI":"10.3390\/rs13142729","article-title":"A Novel Motion Compensation Scheme for Airborne Very High Resolution SAR","volume":"13","author":"Chen","year":"2021","journal-title":"Remote Sens."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2670","DOI":"10.3390\/rs14112670","article-title":"An Improved Spatially Variant MOCO Approach Based on an MDA for High-Resolution UAV SAR Imaging with Large Measurement Errors","volume":"14","author":"Ren","year":"2022","journal-title":"Remote Sens."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"792","DOI":"10.1109\/LGRS.2016.2544945","article-title":"Compensation for high-frequency vibration of platform in SAR imaging based on adaptive chirplet decomposition","volume":"13","author":"Wang","year":"2016","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2669","DOI":"10.3390\/s20092669","article-title":"A novel high-frequency vibration error estimation and compensation algorithm for THz-SAR imaging based on local FrFT","volume":"20","author":"Li","year":"2020","journal-title":"Sensors"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1238","DOI":"10.1109\/LSP.2017.2715832","article-title":"Parameter Estimation of Hybrid Linear Frequency Modulation-Sinusoidal Frequency Modulation Signal","volume":"24","author":"Wang","year":"2017","journal-title":"IEEE Signal Processing Lett."},{"key":"ref_13","first-page":"6951","article-title":"Method for High-resolution SAR Imaging Based on Inverse Radon Transform","volume":"20","author":"Wang","year":"2019","journal-title":"J. Eng."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Wang, Z., Wang, Y., and Xu, L. (2017, January 14\u201317). Time-Frequency Ridge-based Parameter Estimation for Sinusoidal Frequency Modulation Signals. Proceedings of the International Conference in Communications, Signal Processing, and Systems (CSPS), Harbin, China.","DOI":"10.1007\/978-981-10-6571-2_165"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Xia, H., Chen, Q., Li, Y., Fu, C., and Wang, H. (2018, January 10\u201312). A high frequency vibration compensation approach in terahertz SAR based on wavelet multi-resolution analysis. Proceedings of the Inter-American Social Security Conference (CISS), Shanghai, China.","DOI":"10.1109\/SARS.2018.8552000"},{"key":"ref_16","first-page":"1","article-title":"Target vibration estimation in SAR based on phaseanalysis method","volume":"94","author":"Xia","year":"2016","journal-title":"EURASIP J. Adv. Signal Processing"},{"key":"ref_17","first-page":"1973","article-title":"Parameter estimation of multicomponent SFM signals based on discrete sinusoidal frequency modulation transform","volume":"34","author":"Sun","year":"2012","journal-title":"Syst. Eng. Electron."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"6333","DOI":"10.1109\/JSEN.2016.2584622","article-title":"Enhancement of azimuth focus performance in high-resolution SAR imaging based on the compensation for sensors platform vibration","volume":"16","author":"Wang","year":"2016","journal-title":"IEEE Sens. J."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"020502","DOI":"10.1117\/1.JRS.10.020502","article-title":"Parameters Estimation of Sinusoidal Frequency Modulation Signal with Application in Synthetic Aperture Radar Imaging","volume":"10","author":"Wang","year":"2016","journal-title":"J. Appl. Remote Sens."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"7593","DOI":"10.1109\/TGRS.2014.2314681","article-title":"SAR-based paired echo focusing and suppression of vibrating targets","volume":"52","author":"Zhang","year":"2014","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"5485","DOI":"10.1109\/ACCESS.2020.3047856","article-title":"Estimation of High-Frequency Vibration Parameters for Terahertz SAR Imaging Based on FrFT With Combination of QML and RANSAC","volume":"9","author":"Li","year":"2021","journal-title":"IEEE Access"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1460","DOI":"10.1109\/TAES.2016.140615","article-title":"High-frequency vibration compensation of helicopter-borne THz-SAR","volume":"52","author":"Zhang","year":"2016","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_23","first-page":"1","article-title":"Vibration Compensation of Airborne Terahertz SAR Based on Along Track Interferometry","volume":"19","author":"Sun","year":"2022","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Charvat, G.L. (2014). Small and Short-Range Radar Systems, CRC Press.","DOI":"10.1201\/b16718"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2017\/5852171","article-title":"Sinusoidal frequency modulation Fourier-Bessel series for multicomponent SFM signal estimation and separation","volume":"2017","author":"He","year":"2017","journal-title":"Math. Probl. Eng."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1297","DOI":"10.1016\/j.jspi.2007.04.024","article-title":"Sequential estimation of the sum of sinusoidal model parameters","volume":"138","author":"Prasad","year":"2008","journal-title":"J. Stat. Plan. Inference"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1111\/j.2517-6161.1961.tb00430.x","article-title":"A Method of Maximum-Likelihood Estimation","volume":"23","author":"Richards","year":"1961","journal-title":"J. R. Stat. Soc. Ser. B Methodol."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Wang, J., Li, Y., Song, M., Huang, P., and Xing, M. (2022). Noise Robust High-Speed Motion Compensation for ISAR Imaging Based on Parametric Minimum Entropy Optimization. Remote Sens., 14.","DOI":"10.3390\/rs14092178"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Jia, X., Song, H., and He, W. (2021). A Novel Method for Refocusing Moving Ships in SAR Images via ISAR Technique. Remote Sens., 13.","DOI":"10.3390\/rs13142738"}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/14\/3416\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:51:56Z","timestamp":1760140316000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/14\/3416"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,7,16]]},"references-count":29,"journal-issue":{"issue":"14","published-online":{"date-parts":[[2022,7]]}},"alternative-id":["rs14143416"],"URL":"https:\/\/doi.org\/10.3390\/rs14143416","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2022,7,16]]}}}