{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:07:43Z","timestamp":1760234863809,"version":"build-2065373602"},"reference-count":34,"publisher":"MDPI AG","issue":"13","license":[{"start":{"date-parts":[[2021,6,30]],"date-time":"2021-06-30T00:00:00Z","timestamp":1625011200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["2019M660049XB"],"award-info":[{"award-number":["2019M660049XB"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Fundamental Research Funds for the Central Universities, CHD","award":["300102240302"],"award-info":[{"award-number":["300102240302"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61871059 and  61901057"],"award-info":[{"award-number":["61871059 and  61901057"]}],"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>Recently, numerous reconstruction-based adaptive beamformers have been proposed, which can improve the quality of imaging or localization in the application of passive synthetic aperture (PSA) sensing. However, when the trajectory is curvilinear, existing beamformers may not be robust enough to suppress interferences efficiently. To overcome the model mismatch of unknown curvilinear trajectory, this paper presents an adaptive beamforming algorithm by reconstructing the interference-plus-noise covariance matrix (INCM). Using the idea of signal subspace fitting, we construct a joint optimization problem, where the unknown directions of arrival (DOAs) and array shape parameters are coupled together. To tackle this problem, we develop a hybrid optimization method by combining the genetic algorithm and difference-based quasi-Newton method. Then, a set of non-orthogonal bases for signal subspace is estimated with an acceptable computational complexity. Instead of reconstructing the covariance matrix by integrating the spatial spectrum over interference angular sector, we extract the desired signal covariance matrix (DSCM) directly from signal subspace, and then the INCM is reconstructed by eliminating DSCM from the sample covariance matrix (SCM). Numerical simulations demonstrate the robustness of the proposed beamformer in the case of signal direction error, local scattering and random curvilinear trajectory.<\/jats:p>","DOI":"10.3390\/rs13132562","type":"journal-article","created":{"date-parts":[[2021,7,1]],"date-time":"2021-07-01T02:44:39Z","timestamp":1625107479000},"page":"2562","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Adaptive Beamforming for Passive Synthetic Aperture with Uncertain Curvilinear Trajectory"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6581-2304","authenticated-orcid":false,"given":"Peng","family":"Chen","sequence":"first","affiliation":[{"name":"School of Information Engineering, Chang\u2019an University, Xi\u2019an 710064, China"}]},{"given":"Long","family":"Zuo","sequence":"additional","affiliation":[{"name":"School of Information Engineering, Chang\u2019an University, Xi\u2019an 710064, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1675-1445","authenticated-orcid":false,"given":"Wei","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Information Engineering, Chang\u2019an University, Xi\u2019an 710064, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,6,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"EL255","DOI":"10.1121\/1.4915003","article-title":"Localization of low-frequency coherent sound sources with compressive beamforming-based passive synthetic aperture","volume":"137","author":"Lei","year":"2015","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Wang, L., Bai, X., Chen, G., and Zhou, F. (2021). Hybrid Inference Network for Few-Shot SAR Automatic Target Recognition. IEEE Trans. Geosci. Remote Sens., 1\u201313.","DOI":"10.1109\/TGRS.2021.3124336"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1109\/TGRS.2019.2936246","article-title":"Focusing Hypersonic Vehicle-Borne SAR Data Using Radius\/Angle Algorithm","volume":"58","author":"Tang","year":"2020","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"372","DOI":"10.1109\/LSP.2018.2890764","article-title":"Sensor Localization for Highly Deformed Partially Calibrated Arrays With Moving Targets","volume":"26","author":"Yang","year":"2019","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1408","DOI":"10.1109\/PROC.1969.7278","article-title":"High-resolution frequency-wavenumber spectrum analysis","volume":"57","author":"Capon","year":"1969","journal-title":"Proc. IEEE"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1365","DOI":"10.1109\/TASSP.1987.1165054","article-title":"Robust adaptive beamforming","volume":"35","author":"Cox","year":"1987","journal-title":"IEEE Trans. Acoust. Speech Signal Process."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"172","DOI":"10.1109\/LSP.2003.811637","article-title":"Robust Capon beamforming","volume":"10","author":"Stoica","year":"2003","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1109\/TSP.2002.806865","article-title":"Robust adaptive beamforming using worst-case performance optimization: A solution to the signal mismatch problem","volume":"51","author":"Vorobyov","year":"2003","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"5719","DOI":"10.1109\/TSP.2008.929866","article-title":"On the relationship between robust minimum variance beamformers with probabilistic and worst-case distortionless response constraints","volume":"56","author":"Vorobyov","year":"2008","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"62","DOI":"10.1109\/MSP.2010.936015","article-title":"Convex optimization-based beamforming","volume":"27","author":"Gershman","year":"2010","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"5845","DOI":"10.1109\/TSP.2012.2212889","article-title":"Linearly constrained robust capon beamforming","volume":"60","author":"Somasundaram","year":"2012","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1601","DOI":"10.1109\/TSP.2010.2096222","article-title":"Iterative robust minimum variance beamforming","volume":"59","author":"Nai","year":"2011","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"37","DOI":"10.2528\/PIERL11040104","article-title":"Robust adaptive beamforming based on covariance matrix reconstruction for look direction mismatch","volume":"25","author":"Mallipeddi","year":"2011","journal-title":"Prog. Electromagn. Res. Lett."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"3881","DOI":"10.1109\/TSP.2012.2194289","article-title":"Robust adaptive beamforming based on interference covariance matrix reconstruction and steering vector estimation","volume":"60","author":"Gu","year":"2012","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1099","DOI":"10.1109\/TVT.2017.2704610","article-title":"A robust and efficient algorithm for coprime array adaptive beamforming","volume":"67","author":"Zhou","year":"2018","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"3919","DOI":"10.1109\/TSP.2016.2550006","article-title":"Robust adaptive beamforming based on low-rank and cross-correlation techniques","volume":"64","author":"Ruan","year":"2016","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1016\/j.sigpro.2016.07.008","article-title":"Robust adaptive beamforming via a novel subspace method for interference covariance matrix reconstruction","volume":"130","author":"Yuan","year":"2017","journal-title":"Signal Process."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"845","DOI":"10.1109\/LSP.2020.2994527","article-title":"Maximum Entropy-Based Interference-Plus-Noise Covariance Matrix Reconstruction for Robust Adaptive Beamforming","volume":"27","author":"Mohammadzadeh","year":"2020","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"107939","DOI":"10.1016\/j.sigpro.2020.107939","article-title":"Robust adaptive beamforming based on a method for steering vector estimation and interference covariance matrix reconstruction","volume":"182","author":"Sun","year":"2021","journal-title":"Signal Process."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1007\/s00034-020-01481-z","article-title":"Adaptive Beamforming via Desired Signal Robust Removal for Interference-Plus-Noise Covariance Matrix Reconstruction","volume":"40","author":"Zhang","year":"2021","journal-title":"Circuits Syst. Signal Process."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1007\/s11045-020-00737-w","article-title":"An uncertainty-set-shrinkage-based covariance matrix reconstruction algorithm for robust adaptive beamforming","volume":"32","author":"Chen","year":"2020","journal-title":"Multidimens. Syst. Signal Process."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Chen, P., Yang, Y., Wang, Y., and Ma, Y. (2018). Robust adaptive beamforming with sensor position errors using weighted subspace fitting-based covariance matrix reconstruction. Sensors, 18.","DOI":"10.3390\/s18051476"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1109\/48.126976","article-title":"Calculation of the shape of a towed underwater acoustic array","volume":"17","author":"Howard","year":"1992","journal-title":"IEEE J. Ocean. Eng."},{"key":"ref_24","first-page":"593","article-title":"Evaluation of the calibration method using iterative spline interpolation for array shape estimation","volume":"2","author":"Park","year":"2004","journal-title":"Ocean. Conf."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1565","DOI":"10.1121\/1.402437","article-title":"Comparison of Sharpness and Eigenvector Methods for Towed Array Shape Estimation","volume":"91","author":"Ferguson","year":"1992","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"827","DOI":"10.1109\/8.509886","article-title":"Sensor-array calibration using a maximum-likelihood approach","volume":"44","author":"Ng","year":"1996","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"847","DOI":"10.1109\/JOE.2004.833373","article-title":"Generalization of the subspace-based array shape estimations","volume":"29","author":"Park","year":"2004","journal-title":"IEEE J. Ocean. Eng."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1109\/JOE.2008.923556","article-title":"A Simplified Subspace Fitting Method for Estimating Shape of a Towed Array","volume":"33","author":"Chungyong","year":"2008","journal-title":"IEEE J. Ocean. Eng."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1016\/0165-1684(91)90013-9","article-title":"Array shape calibration using eigenstructure methods","volume":"22","author":"Weiss","year":"1991","journal-title":"Signal Process."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"2201","DOI":"10.1016\/S0165-1684(01)00121-9","article-title":"Array self-calibration with large sensor position errors","volume":"81","author":"Flanagan","year":"2001","journal-title":"Signal Process."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1109\/LSP.2018.2878948","article-title":"Adaptive Beamforming with Sensor Position Errors Using Covariance Matrix Construction Based on Subspace Bases Transition","volume":"26","author":"Chen","year":"2019","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"8495","DOI":"10.1109\/TVT.2018.2849646","article-title":"Covariance Matrix Reconstruction With Interference Steering Vector and Power Estimation for Robust Adaptive Beamforming","volume":"67","author":"Zheng","year":"2018","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_33","unstructured":"Goldberg, D.E. (1989). Genetic Algorithms in Search, Optimization, and Machine Learning, Addison-Wesley Pub. Co."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1872","DOI":"10.1109\/78.847774","article-title":"Decoupled estimation of DOA and angular spread for a spatially distributed source","volume":"48","author":"Besson","year":"2000","journal-title":"IEEE Trans. Signal Process."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/13\/2562\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:24:03Z","timestamp":1760163843000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/13\/2562"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,6,30]]},"references-count":34,"journal-issue":{"issue":"13","published-online":{"date-parts":[[2021,7]]}},"alternative-id":["rs13132562"],"URL":"https:\/\/doi.org\/10.3390\/rs13132562","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2021,6,30]]}}}