{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:17:49Z","timestamp":1760145469329,"version":"build-2065373602"},"reference-count":40,"publisher":"MDPI AG","issue":"15","license":[{"start":{"date-parts":[[2024,8,2]],"date-time":"2024-08-02T00:00:00Z","timestamp":1722556800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Key R&amp;D Program of China","doi-asserted-by":"publisher","award":["2022YFB3901601","62201554"],"award-info":[{"award-number":["2022YFB3901601","62201554"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["2022YFB3901601","62201554"],"award-info":[{"award-number":["2022YFB3901601","62201554"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>The measurement of the target azimuth angle using forward-looking radar (FLR) is widely applied in unmanned systems, such as obstacle avoidance and tracking applications. This paper proposes a semi-supervised support vector regression (SVR) method to solve the problem of small sample learning of the target angle with FLR. This method utilizes function approximation to solve the problem of estimating the target angle. First, SVR is used to construct the function mapping relationship between the echo and the target angle in beamspace. Next, by adding manifold constraints to the loss function, supervised learning is extended to semi-supervised learning, aiming to improve the small sample adaptation ability. This framework supports updating the angle estimating function with continuously increasing unlabeled samples during the FLR scanning process. The numerical simulation results show that the new technology has better performance than model-based methods and fully supervised methods, especially under limited conditions such as signal-to-noise ratio and number of training samples.<\/jats:p>","DOI":"10.3390\/rs16152840","type":"journal-article","created":{"date-parts":[[2024,8,2]],"date-time":"2024-08-02T13:14:42Z","timestamp":1722604482000},"page":"2840","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Angle Estimation Using Learning-Based Doppler Deconvolution in Beamspace with Forward-Looking Radar"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0029-1368","authenticated-orcid":false,"given":"Wenjie","family":"Li","sequence":"first","affiliation":[{"name":"National Key Laboratory of Microwave Imaging, Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100190, China"},{"name":"School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-6326-4552","authenticated-orcid":false,"given":"Xinhao","family":"Xu","sequence":"additional","affiliation":[{"name":"National Key Laboratory of Microwave Imaging, Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100190, China"},{"name":"School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3333-0394","authenticated-orcid":false,"given":"Yihao","family":"Xu","sequence":"additional","affiliation":[{"name":"National Key Laboratory of Microwave Imaging, Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100190, China"},{"name":"School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-6562-4709","authenticated-orcid":false,"given":"Yuchen","family":"Luan","sequence":"additional","affiliation":[{"name":"National Key Laboratory of Microwave Imaging, Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100190, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haibo","family":"Tang","sequence":"additional","affiliation":[{"name":"National Key Laboratory of Microwave Imaging, Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100190, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Longyong","family":"Chen","sequence":"additional","affiliation":[{"name":"National Key Laboratory of Microwave Imaging, Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100190, China"},{"name":"School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fubo","family":"Zhang","sequence":"additional","affiliation":[{"name":"National Key Laboratory of Microwave Imaging, Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100190, China"},{"name":"School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jie","family":"Liu","sequence":"additional","affiliation":[{"name":"The 27th Research Institute of China Electronics Technology Group Corporation, Zhengzhou 450047, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Junming","family":"Yu","sequence":"additional","affiliation":[{"name":"The 27th Research Institute of China Electronics Technology Group Corporation, Zhengzhou 450047, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,8,2]]},"reference":[{"key":"ref_1","first-page":"1","article-title":"Bayesian Forward-Looking Superresolution Imaging Using Doppler Deconvolution in Expanded Beam Space for High-Speed Platform","volume":"60","author":"Chen","year":"2022","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"846","DOI":"10.1109\/LGRS.2016.2550491","article-title":"Angular Superresolution for Scanning Radar with Improved Regularized Iterative Adaptive Approach","volume":"13","author":"Zhang","year":"2016","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"863","DOI":"10.1049\/el.2014.3978","article-title":"Sparse Super-resolution Imaging for Airborne Single Channel Forward-looking Radar in Expanded Beam Space via l p  Regularisation","volume":"51","author":"Chen","year":"2015","journal-title":"Electron. Lett."},{"key":"ref_4","unstructured":"Dropkin, H., and Ly, C. (1997, January 13\u201315). Superresolution for scanning antenna. Proceedings of the 1997 IEEE National Radar Conference, Syracuse, New York, NY, USA."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"3103","DOI":"10.1109\/TAES.2019.2900133","article-title":"Angular Superresol for Signal Model in Coherent Scanning Radars","volume":"55","author":"Li","year":"2019","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1109\/TGRS.2017.2743263","article-title":"Super-Resolution Surface Mapping for Scanning Radar: Inverse Filtering Based on the Fast Iterative Adaptive Approach","volume":"56","author":"Zhang","year":"2018","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_7","first-page":"6055","article-title":"Wideband Sparse Reconstruction for Scanning Radar","volume":"56","author":"Zhang","year":"2018","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Zhu, R., Wen, J., and Xiong, X. (2020, January 28\u201331). Forward-looking imaging algorithm for airborne radar based on beam-space multiple signal classification. Proceedings of the 2020 IEEE 20th International Conference on Communication Technology (ICCT), Nanning, China.","DOI":"10.1109\/ICCT50939.2020.9295943"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"6924","DOI":"10.3390\/s150306924","article-title":"Bayesian Deconvolution for Angular Super-Resolution in Forward-Looking Scanning Radar","volume":"15","author":"Zha","year":"2015","journal-title":"Sensors"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2822","DOI":"10.1109\/JSTARS.2019.2918189","article-title":"Sea-Surface Target Angular Superresolution in Forward-Looking Radar Imaging Based on Maximum A Posteriori Algorithm","volume":"12","author":"Zhang","year":"2019","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2032","DOI":"10.1109\/JSTARS.2019.2912993","article-title":"Azimuth Superresolution of Forward-Looking Radar Imaging Which Relies on Linearized Bregman","volume":"12","author":"Zhang","year":"2019","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"13419","DOI":"10.1109\/ACCESS.2020.2965973","article-title":"A Bayesian angular superresolution method with lognormal constraint for sea-surface target","volume":"8","author":"Yang","year":"2020","journal-title":"IEEE Access"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1016\/j.acha.2012.08.003","article-title":"Spectral compressive sensing","volume":"35","author":"Duarte","year":"2013","journal-title":"Appl. Comput. Harmon. Anal."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2182","DOI":"10.1109\/TSP.2011.2112650","article-title":"Sensitivity to basis mismatch in compressed sensing","volume":"59","author":"Chi","year":"2011","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"342","DOI":"10.1109\/JSTSP.2009.2039170","article-title":"General deviants: An analysis of perturbations in compressed sensing","volume":"4","author":"Herman","year":"2010","journal-title":"IEEE J. Sel. Top. Signal Process."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"631","DOI":"10.1016\/j.neucom.2007.08.023","article-title":"A RBFNN Approach for DoA Estimation of Ultra Wideband Antenna Array","volume":"71","author":"Wang","year":"2008","journal-title":"Neurocomputing"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Xiao, X., Zhao, S., Zhong, X., Jones, D.L., Chng, E.S., and Li, H. (2015, January 19\u201324). A Learning-Based Approach to Direction of Arrival Estimation in Noisy and Reverberant Environments. Proceedings of the 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), South Brisbane, QLD, Australia.","DOI":"10.1109\/ICASSP.2015.7178484"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Chakrabarty, S., and Habets, E.A.P. (2017, January 15\u201318). Broadband Doa Estimation Using Convolutional Neural Networks Trained with Noise Signals. Proceedings of the 2017 IEEE Workshop on Applications of Signal Processing to Audio and Acoustics (WASPAA), New Paltz, NY, USA.","DOI":"10.1109\/WASPAA.2017.8170010"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"6403","DOI":"10.1109\/TIE.2017.2786219","article-title":"Indoor Sound Source Localization with Probabilistic Neural Network","volume":"65","author":"Sun","year":"2018","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"7315","DOI":"10.1109\/TAP.2018.2874430","article-title":"Direction-of-Arrival Estimation Based on Deep Neural Networks with Robustness to Array Imperfections","volume":"66","author":"Liu","year":"2018","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1109\/97.300315","article-title":"Radial Basis Function Neural Network for Direction-of-Arrivals Estimation","volume":"1","author":"Lo","year":"1994","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"768","DOI":"10.1109\/8.855496","article-title":"A Neural Network-Based Smart Antenna for Multiple Source Tracking","volume":"48","author":"Christodoulou","year":"2000","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1109\/LAWP.2007.903491","article-title":"Direction of Arrival Estimation Based on Support Vector Regression: Experimental Validation and Comparison with MUSIC","volume":"6","author":"Randazzo","year":"2007","journal-title":"IEEE Antennas Wirel. Propag. Lett."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Dehghanpour, M., Vakili, V.T., and Farrokhi, A. (2012, January 19\u201321). DOA Estimation Using Multiple Kernel Learning SVM Considering Mutual Coupling. Proceedings of the 2012 Fourth International Conference on Intelligent Networking and Collaborative Systems, Bucharest, Romania.","DOI":"10.1109\/iNCoS.2012.112"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Ashok, C., and Venkateswaran, N. (2016, January 23\u201325). Support Vector Regression Based DOA Estimation in Heavy Tailed Noise Environment. Proceedings of the 2016 International Conference on Wireless Communications, Signal Processing and Networking (WiSPNET), Chennai, India.","DOI":"10.1109\/WiSPNET.2016.7566099"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Venkateswaran, N., and Ashok, C. (2016, January 22\u201325). DOA Estimation of Near-Field Sources Using Support Vector Regression. Proceedings of the 2016 IEEE Region 10 Conference (TENCON), Singapore.","DOI":"10.1109\/TENCON.2016.7848281"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2569","DOI":"10.1109\/TVT.2008.2005723","article-title":"Target Tracking Using Particle Filters with Support Vector Regression","volume":"58","author":"Kabaoglu","year":"2009","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_28","unstructured":"Ozer, S., Cirpan, H., and Kabaoglu, N. (2006, January 17\u201319). Support Vector Machines Based Target Tracking Techniques. Proceedings of the 2006 IEEE 14th Signal Processing and Communications Applications, Antalya, Turkey."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2804","DOI":"10.1016\/j.sigpro.2008.06.006","article-title":"Wideband Target Tracking by Using SVR-based Sequential Monte Carlo Method","volume":"88","year":"2008","journal-title":"Signal Process."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"642","DOI":"10.1109\/LSP.2019.2901641","article-title":"Coherent SVR Learning for Wideband Direction-of-Arrival Estimation","volume":"26","author":"Wu","year":"2019","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_31","unstructured":"Wu, L. (2022). Array Signal Processing Based on Machine Learning. [Ph.D. Thesis, National University of Defense Technology]."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Perry, R.P., DiPietro, R.C., and Fante, R.L. (2007, January 17\u201320). Coherent Integration with Range Migration Using Keystone Formatting. Proceedings of the 2007 IEEE Radar Conference, Waltham, MA, USA.","DOI":"10.1109\/RADAR.2007.374333"},{"key":"ref_33","first-page":"1","article-title":"Real aperture radar forward-looking imaging based on variational Bayesian in presence of outliers","volume":"60","author":"Li","year":"2022","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Chen, H., Wang, Z., Zhang, Y., Jin, X., Gao, W., and Yu, J. (2023). Data-driven airborne bayesian forward-looking superresolution imaging based on generalized Gaussian distribution. Front. Signal Process., 3.","DOI":"10.3389\/frsip.2023.1093203"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"827","DOI":"10.1109\/LSP.2005.859517","article-title":"A generalized MVDR spectrum","volume":"12","author":"Benesty","year":"2005","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"575","DOI":"10.2528\/PIER13101804","article-title":"Forward-looking imaging of scanning phased array radar based on the compressed sensing","volume":"143","author":"Wen","year":"2013","journal-title":"Prog. Electromagn. Res."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"902","DOI":"10.1109\/TNNLS.2012.2190420","article-title":"Laplacian Embedded Regression for Scalable Manifold Regularization","volume":"23","author":"Chen","year":"2012","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_38","first-page":"564","article-title":"Support Vector Regression Methods for Functional Data","volume":"Volume 4756","author":"Rueda","year":"2008","journal-title":"Progress in Pattern Recognition, Image Analysis and Applications"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1016\/j.neucom.2018.05.065","article-title":"Least Squares Kernel Ensemble Regression in Reproducing Kernel Hilbert Space","volume":"311","author":"Shen","year":"2018","journal-title":"Neurocomputing"},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Beale, R., and Jackson, T. (1990). Neural Computing\u2014An Introduction, CRC Press.","DOI":"10.1887\/0852742622"}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/16\/15\/2840\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T15:28:55Z","timestamp":1760110135000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/16\/15\/2840"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,8,2]]},"references-count":40,"journal-issue":{"issue":"15","published-online":{"date-parts":[[2024,8]]}},"alternative-id":["rs16152840"],"URL":"https:\/\/doi.org\/10.3390\/rs16152840","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2024,8,2]]}}}