{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:20:10Z","timestamp":1760149210173,"version":"build-2065373602"},"reference-count":41,"publisher":"MDPI AG","issue":"13","license":[{"start":{"date-parts":[[2023,7,6]],"date-time":"2023-07-06T00:00:00Z","timestamp":1688601600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Important Science and Technology of Hainan Province","award":["ZDKJ202010","61961013","62101088"],"award-info":[{"award-number":["ZDKJ202010","61961013","62101088"]}]},{"name":"National Natural Science Foundation of China","award":["ZDKJ202010","61961013","62101088"],"award-info":[{"award-number":["ZDKJ202010","61961013","62101088"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In the environment of unknown mutual coupling, many works on direction-of-arrival (DOA) estimation with sensor array are prone to performance degradation or even failure. Moreover, there are few literatures on off-grid direction finding using regularized sparse recovery technology. Therefore, the scenario of off-grid DOA estimation in sensor array with unknown mutual coupling is investigated, and then a reweighted off-grid Sparse Spectrum Fitting (Re-OGSpSF) approach is developed in this article. Inspired by the selection matrix, an undisturbed array output is formed to remove the unknown mutual coupling effect. Subsequently, a refined off-grid SpSF (OGSpSF) recovery model is structured by integrating the off-grid error term obtained from the first-order Taylor approximation of the higher-order term into the underlying on-grid sparse representation model. After that, a novel Re-OGSpSF framework is formulated to recover the sparse vectors, where a weighted matrix is developed by the MUSIC-like spectrum function to enhance the solution\u2019s sparsity. Ultimately, off-grid DOA estimation can be realized with the help of the recovered sparse vectors. Thanks to the off-grid representation and reweighted strategy, the proposed method can effectively and efficiently achieve high-precision continuous DOA estimation, making it favorable for real-time direction finding. The simulation results validate the superiority of the proposed method.<\/jats:p>","DOI":"10.3390\/s23136196","type":"journal-article","created":{"date-parts":[[2023,7,7]],"date-time":"2023-07-07T01:57:09Z","timestamp":1688695029000},"page":"6196","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Reweighted Off-Grid Sparse Spectrum Fitting for DOA Estimation in Sensor Array with Unknown Mutual Coupling"],"prefix":"10.3390","volume":"23","author":[{"given":"Liangliang","family":"Li","sequence":"first","affiliation":[{"name":"State Key Laboratory of Marine Resource Utilization in South China Sea, School of Information and Communication Engineering, Hainan University, Haikou 570228, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6681-6489","authenticated-orcid":false,"given":"Xianpeng","family":"Wang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Marine Resource Utilization in South China Sea, School of Information and Communication Engineering, Hainan University, Haikou 570228, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4769-3639","authenticated-orcid":false,"given":"Xiang","family":"Lan","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Marine Resource Utilization in South China Sea, School of Information and Communication Engineering, Hainan University, Haikou 570228, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9875-051X","authenticated-orcid":false,"given":"Gang","family":"Xu","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Millimeter Waves, Southeast University, Nanjing 210096, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Liangtian","family":"Wan","sequence":"additional","affiliation":[{"name":"Key Laboratory for Ubiquitous Network and Service Software of Liaoning Province, School of Software, Dalian University of Technology, Dalian 116620, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,7,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"573","DOI":"10.1109\/TAES.2020.3034012","article-title":"Nested MIMO Radar: Coarrays, Tensor Modeling, and Angle Estimation","volume":"57","author":"Shi","year":"2021","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"21561","DOI":"10.1109\/JIOT.2022.3181450","article-title":"Source Direction Finding and Direct Localization Exploiting UAV Array With Unknown Gain-Phase Errors","volume":"9","author":"Li","year":"2022","journal-title":"IEEE Internet Things J."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"815","DOI":"10.1109\/JIOT.2022.3204267","article-title":"3-D Positioning Method for Anonymous UAV Based on Bistatic Polarized MIMO Radar","volume":"10","author":"Wen","year":"2023","journal-title":"IEEE Internet Things J."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1109\/LSP.2021.3121626","article-title":"An Efficient Method for Cooperative Multi-Target Localization in Automotive Radar","volume":"29","author":"Zhang","year":"2022","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_5","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 Propagat."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"984","DOI":"10.1109\/29.32276","article-title":"Esprit-estimation of signal parameters via rotational invariance techniques","volume":"37","author":"Roy","year":"1989","journal-title":"IEEE Trans. Acoust. Speech Signal Process."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1422","DOI":"10.1109\/LCOMM.2018.2837049","article-title":"Localization of near-field sources: A reduced-dimension music algorithm","volume":"22","author":"Zhang","year":"2018","journal-title":"IEEE Commun. Lett."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2375","DOI":"10.1109\/LCOMM.2021.3075208","article-title":"An Improved ESPRIT-Based Algorithm for Monostatic FDA-MIMO Radar With Linear or Nonlinear Frequency Increments","volume":"25","author":"Feng","year":"2021","journal-title":"IEEE Commun. Lett."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"44433","DOI":"10.1109\/ACCESS.2018.2862435","article-title":"Dimension-Reduced Direction-of-Arrival Estimation Based on l2,1-Norm Penalty","volume":"6","author":"Liu","year":"2018","journal-title":"IEEE Access"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"28271","DOI":"10.3390\/s151128271","article-title":"Real-valued covariance vector sparsity-inducing DOA estimation for monostatic MIMO radar","volume":"15","author":"Wang","year":"2015","journal-title":"Sensors"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1006\/dspr.1998.0316","article-title":"Covariance matching estimation techniques for array signal processing applications","volume":"8","author":"Ottersten","year":"1998","journal-title":"Digit. Signal Process."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Shin, M., Hong, W., Lee, K., and Choo, Y. (2022). Passive Sonar Target Identification Using Multiple-Measurement Sparse Bayesian Learning. Sensors, 22.","DOI":"10.3390\/s22218511"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"4977","DOI":"10.1109\/TSP.2021.3106741","article-title":"Real-Valued Sparse Bayesian Learning for DOA Estimation With Arbitrary Linear Arrays","volume":"69","author":"Dai","year":"2021","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_14","first-page":"1","article-title":"Structured Low-Rank and Sparse Method for ISAR Imaging With 2-D Compressive Sampling","volume":"60","author":"Xu","year":"2022","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1109\/MGRS.2022.3218801","article-title":"Sparse Synthetic Aperture Radar Imaging from Compressed Sensing and Machine Learning: Theories, Applications and Trends","volume":"10","author":"Xu","year":"2022","journal-title":"IEEE Geosci. Remote Sens. Mag."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"258","DOI":"10.1016\/j.sigpro.2014.04.007","article-title":"A sparse representation scheme for angle estimation in monostatic mimo radar","volume":"104","author":"Wang","year":"2014","journal-title":"Signal Process."},{"key":"ref_17","unstructured":"Zheng, J. (2013). Sparse Spectrum Fitting in Array Processing. [Ph.D. Thesis, University of Minnesota]."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1109\/TSP.2012.2222378","article-title":"Off-grid direction of arrival estimation using sparse bayesian inference","volume":"61","author":"Yang","year":"2013","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1016\/j.sigpro.2013.11.022","article-title":"Off-grid doa estimation using array covariance matrix and block-sparse bayesian learning","volume":"98","author":"Zhang","year":"2014","journal-title":"Signal Process."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1109\/LSP.2016.2636319","article-title":"Root sparse bayesian learning for off-grid doa estimation","volume":"24","author":"Dai","year":"2016","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"268","DOI":"10.1049\/joe.2017.0872","article-title":"Doa estimation for monostatic mimo radar using enhanced sparse bayesian learning","volume":"2018","author":"Wen","year":"2018","journal-title":"J. Eng."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"47500","DOI":"10.1109\/ACCESS.2020.2979055","article-title":"Doa estimation of strictly noncircular sources in wireless sensor array network via block sparse representation","volume":"8","author":"Li","year":"2020","journal-title":"IEEE Access"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Dai, J., Zhao, D., Ye, Z., and Zhang, L. (2010, January 6\u20138). DOA estimation and self-calibration algorithm for nonuniform linear array. Proceedings of the 2010 International Symposium on Intelligent Signal Processing and Communication Systems, Chengdu, China.","DOI":"10.1109\/ISPACS.2010.5704752"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"60645","DOI":"10.1109\/ACCESS.2020.2977221","article-title":"Joint angle estimation and array calibration using eigenspace in monostatic mimo radar","volume":"8","author":"Li","year":"2020","journal-title":"IEEE Access"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1563","DOI":"10.1049\/iet-map.2016.0104","article-title":"Joint direction finding and array calibration method for MIMO radar with unknown gain phase errors","volume":"10","author":"Li","year":"2016","journal-title":"IET Microw. Antennas Propag."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1109\/TAP.2007.915461","article-title":"On the resiliency of music direction finding against antenna sensor coupling","volume":"56","author":"Ye","year":"2008","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"3039","DOI":"10.1016\/j.sigpro.2012.06.013","article-title":"Joint dod and doa estimation of bistatic mimo radar in the presence of unknown mutual coupling","volume":"92","author":"Zheng","year":"2012","journal-title":"Signal Process."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"891","DOI":"10.1109\/TAES.2012.6129676","article-title":"Doa estimation and tracking of ulas with mutual coupling","volume":"48","author":"Liao","year":"2012","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1210","DOI":"10.1109\/LAWP.2012.2223651","article-title":"A sparse representation method for doa estimation with unknown mutual coupling","volume":"11","author":"Dai","year":"2012","journal-title":"IEEE Antennas Wirel. Propag. Lett."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"2622","DOI":"10.1109\/LCOMM.2017.2747547","article-title":"Effective block sparse representation algorithm for doa estimation with unknown mutual coupling","volume":"21","author":"Wang","year":"2017","journal-title":"IEEE Commun. Lett."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Meng, D., Wang, X., Huang, M., Shen, C., and Guo, Y. (2018, January 8\u201311). A sparse representation of array covariance vectors for doa estimation with unknown mutual coupling. Proceedings of the IEEE 18th International Conference on Communication Technology (ICCT), Chongqing, China.","DOI":"10.1109\/ICCT.2018.8599977"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1346","DOI":"10.1049\/el.2018.6844","article-title":"Reweighted l1-norm minimisation for high-resolution doa estimation under unknown mutual coupling","volume":"54","author":"Meng","year":"2018","journal-title":"Electron. Lett."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"5708","DOI":"10.1109\/JIOT.2021.3066504","article-title":"Multi-uav cooperative localization for marine targets based on weighted subspace fitting in sagin environment","volume":"9","author":"Wang","year":"2022","journal-title":"IEEE Internet Things J."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1011","DOI":"10.1177\/0954410015602723","article-title":"Matrix weighted multisensor data fusion for INS\/GNSS\/CNS integration","volume":"230","author":"Hu","year":"2016","journal-title":"Proc. Inst. Mech. Eng. G J. Aerosp. Eng."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1955","DOI":"10.1109\/JSEN.2011.2107896","article-title":"Random weighting method for multi-sensor data fusion","volume":"11","author":"Gao","year":"2011","journal-title":"IEEE Sens. J."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"350","DOI":"10.1016\/j.ins.2014.06.016","article-title":"Windowing-based random weighting fitting of systematic model errors for dynamic vehicle navigation","volume":"282","author":"Gao","year":"2014","journal-title":"Inf. Sci."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1002\/acs.2467","article-title":"Windowing and random weighting\u2014Based adaptive unscented Kalman filter","volume":"29","author":"Gao","year":"2015","journal-title":"Int J. Adapt Control Signal Process."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Wang, H., Wang, X., Huang, M., Cao, C., and Bi, G. (2018, January 19\u201321). Off-grid doa estimation in mutual coupling via robust sparse bayesian learning. Proceedings of the 2018 IEEE 23rd International Conference on Digital Signal Processing (DSP), Shanghai, China.","DOI":"10.1109\/ICDSP.2018.8631610"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"208","DOI":"10.1109\/TSP.2018.2881663","article-title":"Off-grid doa estimation using sparse bayesian learning in mimo radar with unknown mutual coupling","volume":"67","author":"Chen","year":"2018","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.dsp.2019.04.001","article-title":"Sparse off-grid doa estimation method with unknown mutual coupling effect","volume":"90","author":"Chen","year":"2019","journal-title":"Digit. Signal Process."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1109\/8.76322","article-title":"Direction finding in the presence of mutual coupling","volume":"39","author":"Friedlander","year":"1991","journal-title":"IEEE Trans. Antennas Propag."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/13\/6196\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T20:07:22Z","timestamp":1760126842000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/13\/6196"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,7,6]]},"references-count":41,"journal-issue":{"issue":"13","published-online":{"date-parts":[[2023,7]]}},"alternative-id":["s23136196"],"URL":"https:\/\/doi.org\/10.3390\/s23136196","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2023,7,6]]}}}