{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T17:13:00Z","timestamp":1774631580319,"version":"3.50.1"},"reference-count":39,"publisher":"MDPI AG","issue":"17","license":[{"start":{"date-parts":[[2023,8,31]],"date-time":"2023-08-31T00:00:00Z","timestamp":1693440000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Basic Research Program of China","award":["JCKY2021210B073"],"award-info":[{"award-number":["JCKY2021210B073"]}]},{"name":"National Basic Research Program of China","award":["JCKY2022209A001"],"award-info":[{"award-number":["JCKY2022209A001"]}]},{"name":"National Basic Research Program of China","award":["202102010101002"],"award-info":[{"award-number":["202102010101002"]}]},{"name":"National Basic Research Program of China","award":["2022180505"],"award-info":[{"award-number":["2022180505"]}]},{"name":"Key Research and Development Plan of Shanxi Province","award":["JCKY2021210B073"],"award-info":[{"award-number":["JCKY2021210B073"]}]},{"name":"Key Research and Development Plan of Shanxi Province","award":["JCKY2022209A001"],"award-info":[{"award-number":["JCKY2022209A001"]}]},{"name":"Key Research and Development Plan of Shanxi Province","award":["202102010101002"],"award-info":[{"award-number":["202102010101002"]}]},{"name":"Key Research and Development Plan of Shanxi Province","award":["2022180505"],"award-info":[{"award-number":["2022180505"]}]},{"name":"Graduate science and Technology project of the School of Information and Communication Engineering, North University of China","award":["JCKY2021210B073"],"award-info":[{"award-number":["JCKY2021210B073"]}]},{"name":"Graduate science and Technology project of the School of Information and Communication Engineering, North University of China","award":["JCKY2022209A001"],"award-info":[{"award-number":["JCKY2022209A001"]}]},{"name":"Graduate science and Technology project of the School of Information and Communication Engineering, North University of China","award":["202102010101002"],"award-info":[{"award-number":["202102010101002"]}]},{"name":"Graduate science and Technology project of the School of Information and Communication Engineering, North University of China","award":["2022180505"],"award-info":[{"award-number":["2022180505"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Direction of arrival (DOA) estimation is an effective method for detecting various active interference signals during the satellite navigation process. It can be utilized for both interference detection and anti-interference applications. This paper proposes a DOA estimation algorithm for satellite interference sources based on frequency domain covariance matrix reconstruction (FDCMR) to address various types of active interference that may occur in the satellite navigation positioning process. This algorithm can estimate the DOA of coherent signals from multiple frequency points under low signal-to-noise ratio (SNR) conditions. The signals received from the array are transformed from the time domain to the frequency domain using a fast Fourier transform (FFT). The data corresponding to the frequency point of the target signal is extracted from the signal in the frequency domain. The frequency domain covariance matrix of the received array signals is reconstructed by utilizing its covariance matrix property. The spatial spectrum search method is used for the final DOA estimation. Simulation experiments have shown that the proposed algorithm performs well in the DOA estimation under low SNR conditions and also resolves coherency. Moreover, the algorithm\u2019s effectiveness is verified through comparison with three other algorithms. Finally, the algorithm\u2019s applicability is validated through simulations of various interference scenarios.<\/jats:p>","DOI":"10.3390\/s23177575","type":"journal-article","created":{"date-parts":[[2023,8,31]],"date-time":"2023-08-31T11:45:51Z","timestamp":1693482351000},"page":"7575","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Satellite Interference Source Direction of Arrival (DOA) Estimation Based on Frequency Domain Covariance Matrix Reconstruction"],"prefix":"10.3390","volume":"23","author":[{"given":"Jinjie","family":"Yao","sequence":"first","affiliation":[{"name":"Shanxi Key Laboratory of Signal Capturing & Process, North University of China, Taiyuan 030051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Changchun","family":"Zhao","sequence":"additional","affiliation":[{"name":"Shanxi Key Laboratory of Signal Capturing & Process, North University of China, Taiyuan 030051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8715-3939","authenticated-orcid":false,"given":"Jiansheng","family":"Bai","sequence":"additional","affiliation":[{"name":"Shanxi Key Laboratory of Signal Capturing & Process, North University of China, Taiyuan 030051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yang","family":"Ren","sequence":"additional","affiliation":[{"name":"Shanxi Key Laboratory of Signal Capturing & Process, North University of China, Taiyuan 030051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0095-603X","authenticated-orcid":false,"given":"Yangyang","family":"Wang","sequence":"additional","affiliation":[{"name":"Shanxi Key Laboratory of Signal Capturing & Process, North University of China, Taiyuan 030051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jing","family":"Miao","sequence":"additional","affiliation":[{"name":"College of Mechanical Engineering, Suzhou University of Science and Technology, Suzhou 215009, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,8,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1109\/LGRS.2016.2644723","article-title":"Mitigation of Ionospheric Scintillation Effects on GNSS Signals Using Variational Mode Decomposition","volume":"14","author":"Sivavaraprasad","year":"2017","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Su, K., Jin, S., and Hoque, M.M. (2019). Evaluation of Ionospheric Delay Effects on Multi-GNSS Positioning Performance. Remote Sens., 11.","DOI":"10.3390\/rs11020171"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"8287","DOI":"10.1109\/TVT.2023.3252822","article-title":"Outage Probability and Average BER of UAV-Assisted Dual-Hop FSO Communication with Amplify-and-Forward Relaying","volume":"72","author":"Xu","year":"2023","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"4014","DOI":"10.1109\/TCOMM.2018.2818697","article-title":"Mixed RF\/FSO Cooperative Relaying Systems with Co-Channel Interference","volume":"66","author":"Balti","year":"2018","journal-title":"IEEE Trans. Commun."},{"key":"ref_5","unstructured":"Xie, G. (2009). Principles of GPS and Receiver Design, Publishing House of Electronics Industry."},{"key":"ref_6","first-page":"451","article-title":"GPS Anti-Jamming Using Beamforming Technique","volume":"20","author":"Mook","year":"2016","journal-title":"J. Korea Inst. Inf. Commun. Eng."},{"key":"ref_7","first-page":"58","article-title":"GNSS interference analysis and anti-interference technology review","volume":"7","author":"Mei","year":"2021","journal-title":"Chin. Radio"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"4142","DOI":"10.1016\/j.asr.2022.12.035","article-title":"GNSS 2 \u00d7 2 antenna array with beamforming for multipath detection","volume":"71","author":"Matas","year":"2023","journal-title":"Adv. Space Res."},{"key":"ref_9","unstructured":"Konovaltsev, A., Caizzone, S., Cuntz, M., and Meurer, M. (2014, January 8\u201312). Autonomous Spoofing Detection and Mitigation with a Miniaturized Adaptive Antenna Array. Proceedings of the 27th International Technical Meeting of the Satellite Division of the Institute of Navigation, Tampa, FL, USA."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2952","DOI":"10.1109\/JSEN.2018.2797309","article-title":"A Novel Array-Based Spoofing and Jamming Suppression Method for GNSS Receiver","volume":"18","author":"Hu","year":"2018","journal-title":"IEEE Sens. J."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1133316","DOI":"10.3389\/fphy.2023.1133316","article-title":"A survey of GNSS interference monitoring technologies","volume":"11","author":"Qiao","year":"2023","journal-title":"Front. Phys."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1017\/S0373463317000911","article-title":"GNSS threat monitoring and reporting: Past, present, and a proposed future","volume":"71","author":"Thombre","year":"2018","journal-title":"J. Navig."},{"key":"ref_13","first-page":"219","article-title":"Design and implementation of satellite navigation interference monitoring and positioning system","volume":"50","author":"Li","year":"2020","journal-title":"Radio Eng."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"137982","DOI":"10.1109\/ACCESS.2019.2942330","article-title":"UAV-based interference source localization: A multimodal Q-learning approach","volume":"7","author":"Wu","year":"2019","journal-title":"IEEE Access"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"442","DOI":"10.1049\/cje.2021.00.310","article-title":"Remote interference source localization: A multi-UAV-based cooperative framework","volume":"31","author":"Wu","year":"2022","journal-title":"Chin. J. Electron."},{"key":"ref_16","first-page":"79","article-title":"GNSS interference source detection and location technology based on unmanned aerial vehicle","volume":"46","author":"Sun","year":"2021","journal-title":"Gnss World China"},{"key":"ref_17","first-page":"33","article-title":"Beidou weak interference source location method based on adaptive filtering","volume":"41","author":"Li","year":"2022","journal-title":"Foreign Electron. Meas. Technol."},{"key":"ref_18","first-page":"1117","article-title":"High precision direct location method of spoofing interference source in satellite navigation","volume":"50","author":"Liu","year":"2022","journal-title":"J. Electron."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"5238514","DOI":"10.1109\/TGRS.2022.3221934","article-title":"A 3-D sparse SAR imaging method based on Plug-and-Play","volume":"60","author":"Wang","year":"2022","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"905918","DOI":"10.3389\/fphy.2022.905918","article-title":"GNSS Spoofing Suppression Based on Multi-Satellite and Multi-Channel Array Processing","volume":"10","author":"Ni","year":"2022","journal-title":"Front. Phys."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"432","DOI":"10.1109\/TSP.2015.2483481","article-title":"Spatial Filtering of RF Interference in Radio Astronomy Using a Reference Antenna Array","volume":"64","author":"Sardarabadi","year":"2016","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"693","DOI":"10.1109\/TAES.2013.6404136","article-title":"GNSS Multipath Mitigation with a Moving Antenna Array","volume":"49","author":"Daneshmand","year":"2013","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1109\/LMWC.2009.2038517","article-title":"Miniaturized FSS and Patch Antenna Array Coupling for Angle-Independent, High-Order Spatial Filtering","volume":"20","author":"Bayatpur","year":"2010","journal-title":"IEEE Microwave Wirel. Compon. Lett."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1049\/iet-rsn.2017.0416","article-title":"Blind adaptive channel mismatch equalisation method for GNSS antenna arrays","volume":"12","author":"Lu","year":"2018","journal-title":"IET Radar Sonar Navig."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"29909","DOI":"10.1109\/ACCESS.2023.3261671","article-title":"Multiport Beamforming System Based on Reconfigurable Waveguide Phased Antenna Array for Satellite Communication Applications","volume":"11","author":"Wei","year":"2023","journal-title":"IEEE Access"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1109\/MAES.2022.3231580","article-title":"Spaceborne Multibeam Phased Array Antennas for Satellite Communications","volume":"38","author":"Yu","year":"2023","journal-title":"IEEE Aerosp. Electron. Syst. Mag."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"5532","DOI":"10.3390\/s19245532","article-title":"Direction of Arrival Estimation of GPS Narrowband Jammers Using High-Resolution Techniques","volume":"19","author":"Moussa","year":"2019","journal-title":"Sensors"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"3812","DOI":"10.1109\/TAES.2020.2988424","article-title":"DOA Elevation and Azimuth Angles Estimation of GPS Jamming Signals Using Fast Orthogonal Search","volume":"56","author":"Osman","year":"2020","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_29","first-page":"25","article-title":"Compressed sensing DOA estimation method for satellite interference source location","volume":"41","author":"Zhao","year":"2016","journal-title":"Fire Command Control"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"4826","DOI":"10.3390\/rs14194826","article-title":"A Survey of GNSS Spoofing and Anti-Spoofing Technology","volume":"14","author":"Meng","year":"2022","journal-title":"Remote Sens."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1186\/s43020-019-0004-2","article-title":"Research on BeiDou anti-spoofing technology based on comprehensive radio determination satellite service","volume":"1","author":"Wang","year":"2020","journal-title":"Satell. Navig."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"276","DOI":"10.1109\/TAP.1986.1143830","article-title":"Multiple emitter location and signal parameter estimation","volume":"34","author":"Schmidt","year":"1986","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1340","DOI":"10.1109\/TASSP.1986.1164935","article-title":"ESPRIT\u2014A subspace rotation approach to estimation of parameters of cisoids in noise","volume":"34","author":"Roy","year":"1986","journal-title":"IEEE Trans. Acoust. Speech Signal Process."},{"key":"ref_34","first-page":"895","article-title":"A new DOA estimation algorithm based on compressed sensing","volume":"22","author":"Zhang","year":"2019","journal-title":"Clust. Comput. J. Netw. Softw. Tools Appl."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1052","DOI":"10.23919\/JSEE.2022.000103","article-title":"DOA estimation based on multi-frequency joint sparse Bayesian learning for passive radar","volume":"33","author":"Wen","year":"2022","journal-title":"J. Syst. Eng. Electron."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"168","DOI":"10.1186\/1687-6180-2014-168","article-title":"Sparse reconstruction for direction-of-arrival estimation using multi-frequency co-prime arrays","volume":"2014","author":"Ahmad","year":"2014","journal-title":"EURASIP J. Adv. Signal Process."},{"key":"ref_37","unstructured":"Evans, J., Johnson, D., and Sun, D. (1981, January 17\u201318). High resolution angular spectrum estimation techniques for terrain scattering analysis and angle of arrival estimation. Proceedings of the 1st ASSP Workshop Spectral Estimation, Hamiltion, ON, Canada."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1109\/LAWP.2005.860194","article-title":"An ESPRIT-like algorithm for coherent DOA estimation","volume":"4","author":"Han","year":"2005","journal-title":"IEEE Antennas Wirel. Propag. Lett."},{"key":"ref_39","unstructured":"Hu, D.S. (2017). Research on Estimation Algorithm of Wave Direction Based on Compressed Sensing, Harbin Institute of Technology."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/17\/7575\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T20:44:14Z","timestamp":1760129054000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/17\/7575"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,8,31]]},"references-count":39,"journal-issue":{"issue":"17","published-online":{"date-parts":[[2023,9]]}},"alternative-id":["s23177575"],"URL":"https:\/\/doi.org\/10.3390\/s23177575","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,8,31]]}}}