{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,29]],"date-time":"2025-10-29T03:44:22Z","timestamp":1761709462818,"version":"build-2065373602"},"reference-count":35,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2018,4,2]],"date-time":"2018-04-02T00:00:00Z","timestamp":1522627200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Non-Gaussian impulsive noise widely exists in the real world, this paper takes the \u03b1-stable distribution as the mathematical model of non-Gaussian impulsive noise and works on the joint direction-of-arrival (DOA) and range estimation problem of near-field signals in impulsive noise environment. Since the conventional algorithms based on the classical second order correlation statistics degenerate severely in the impulsive noise environment, this paper adopts two robust correlations, the fractional lower order correlation (FLOC) and the nonlinear transform correlation (NTC), and presents two related near-field localization algorithms. In our proposed algorithms, by exploring the symmetrical characteristic of the array, we construct the robust far-field approximate correlation vector in relation with the DOA only, which allows for bearing estimation based on the sparse reconstruction. With the estimated bearing, the range can consequently be obtained by the sparse reconstruction of the output of a virtual array. The proposed algorithms have the merits of good noise suppression ability, and their effectiveness is demonstrated by the computer simulation results.<\/jats:p>","DOI":"10.3390\/s18041066","type":"journal-article","created":{"date-parts":[[2018,4,2]],"date-time":"2018-04-02T12:32:20Z","timestamp":1522672340000},"page":"1066","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Sparse Reconstruction Based Robust Near-Field Source Localization Algorithm"],"prefix":"10.3390","volume":"18","author":[{"given":"Sen","family":"Li","sequence":"first","affiliation":[{"name":"College of Information and Science Technology, Dalian Maritime University, Dalian 116026, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bing","family":"Li","sequence":"additional","affiliation":[{"name":"College of Information and Science Technology, Dalian Maritime University, Dalian 116026, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bin","family":"Lin","sequence":"additional","affiliation":[{"name":"College of Information and Science Technology, Dalian Maritime University, Dalian 116026, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaofang","family":"Tang","sequence":"additional","affiliation":[{"name":"College of Information and Science Technology, Dalian Maritime University, Dalian 116026, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0506-0021","authenticated-orcid":false,"given":"Rongxi","family":"He","sequence":"additional","affiliation":[{"name":"College of Information and Science Technology, Dalian Maritime University, Dalian 116026, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,4,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Guo, R., Zhang, Y., Lin, Q., and Chen, Z. (2016). A Channelization-Based DOA Estimation Method for Wideband Signals. Sensors, 16.","DOI":"10.3390\/s16071031"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1109\/79.526899","article-title":"Two decades of array signal processing research: The parametric approach","volume":"13","author":"Krim","year":"1996","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Tengtrairat, N., and Woo, W.L. (2017, January 2\u20133). Blind 3D sound source direction using stereo microphones based on time-delay estimation and polar-pattern histogram. Proceedings of the 2nd International Conference on Information Technology, Bangkok, Thailand.","DOI":"10.1109\/INCIT.2017.8257881"},{"key":"ref_4","first-page":"42","article-title":"Blind 2D signal direction for limited-sensor space using maximum likelihood estimation","volume":"22","author":"Tengtrairat","year":"2017","journal-title":"Asia Pac. J. Sci. Technol."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"968","DOI":"10.1109\/8.86917","article-title":"Near-field multiple sources localization by passive sensor array","volume":"39","author":"Huang","year":"1991","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"677","DOI":"10.1109\/78.277864","article-title":"Passive localization of near-field sources by path following","volume":"42","author":"Starer","year":"1994","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1407","DOI":"10.1109\/78.757232","article-title":"A modified path-following algorithm using a known algebraic path","volume":"47","author":"Lee","year":"1999","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1109\/LSP.2006.888390","article-title":"Near-field source location via symmetric subarrays","volume":"14","author":"Zhi","year":"2007","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_9","first-page":"1307","article-title":"Near-field source location based on sparse symmetric array","volume":"37","author":"Liang","year":"2009","journal-title":"Acta Electron. Sin."},{"key":"ref_10","first-page":"610","article-title":"A near-field passive localization method","volume":"36","author":"Liu","year":"2007","journal-title":"Infrared Laser Eng."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1109\/TSP.2009.2029723","article-title":"Passive localization of mixed near-field and far-field sources using two-stage music algorithm","volume":"58","author":"Liang","year":"2010","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"3834","DOI":"10.3390\/s150203834","article-title":"Passive localization of mixed far-field and near-field sources without estimating the number of sources","volume":"15","author":"Xie","year":"2015","journal-title":"Sensors"},{"key":"ref_13","unstructured":"Challa, R.N., and Shamsunder, S. (November, January 30). High-order subspace-based algorithms for passive localization of near-field sources. Proceedings of the Twenty-Ninth Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, USA."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"953","DOI":"10.1109\/JSEN.2009.2025580","article-title":"Passive localization of near-field sources using cumulant","volume":"9","author":"Liang","year":"2009","journal-title":"IEEE Sens. J."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1078\/1434-8411-54100135","article-title":"Unconditional maximum likelihood approach for localization of near-field sources: Algorithm and performance analysis","volume":"57","author":"Cekli","year":"2003","journal-title":"AEU Int. J. Electron. Commun."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"3651","DOI":"10.1109\/TSP.2005.855100","article-title":"A weighted linear prediction method for near-field source localization","volume":"53","author":"Grosicki","year":"2005","journal-title":"IEEE Trans. Signal Proc."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"760","DOI":"10.1109\/TAES.2013.6494379","article-title":"DOA estimation for sparse array via sparse signal reconstruction","volume":"49","author":"Hu","year":"2013","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"487","DOI":"10.1109\/LSP.2012.2204248","article-title":"Mixed sources localization based on sparse signal reconstruction","volume":"19","author":"Wang","year":"2012","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"534","DOI":"10.1016\/j.aeue.2013.12.011","article-title":"Passive localization of mixed sources jointly using music and sparse signal reconstruction","volume":"68","author":"Tian","year":"2014","journal-title":"AEU Int. J. Electron. Commun."},{"key":"ref_20","first-page":"1041","article-title":"Near-field sources localization based on sparse signal reconstruction","volume":"42","author":"Lian","year":"2014","journal-title":"Chin. J. Electron."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1260601","DOI":"10.1155\/2017\/1260601","article-title":"Localization of near-field sources based on sparse signal reconstruction with regularization parameter selection","volume":"2017","author":"Li","year":"2017","journal-title":"Int. J. Antennas Propag."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Hu, K., Chepuri, S.P., and Leus, G. (2014, January 22\u201325). Near-field source localization using sparse recovery techniques. Proceedings of the International Conference on Signal Processing and Communications (SPCOM), Bangalore, India.","DOI":"10.1109\/SPCOM.2014.6983929"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Hu, K., Chepuri, S.P., and Leus, G. (2014, January 22\u201325). Near-field source localization: Sparse recovery techniques and grid matching. Proceedings of the IEEE 8th Sensor Array and Multichannel Signal Processing Workshop (SAM), Coru\u00f1a, Spain.","DOI":"10.1109\/SAM.2014.6882418"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Zhang, Y.D., Qin, S., and Amin, M.G. (2015, January 10\u201315). Near-field source localization based on sparse reconstruction of sensor-angle distribution. Proceedings of the IEEE International Radar Conference, Arlington, VA, USA.","DOI":"10.1109\/RADAR.2015.7131121"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"783467","DOI":"10.1155\/2015\/783467","article-title":"Structure-Aware Bayesian Compressive Sensing for Near-Field Source Localization Based on Sensor-Angle Distributions","volume":"2015","author":"Qin","year":"2015","journal-title":"Int. J. Antennas Propag."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"551","DOI":"10.1109\/TVT.2002.1002503","article-title":"Measurement of the impulsive noise environment for satellite-mobile radio systems at 1.5 GHz","volume":"51","author":"Button","year":"2002","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_27","unstructured":"Nikias, C.L., and Shao, M. (1995). Signal Processing with Alpha-Stable Distributions and Applications, Wiely."},{"key":"ref_28","unstructured":"Li, S., He, R.X., Lin, B., and Sun, F. (2016). DOA Estimation Based on Sparse Representation of the Fractional Lower Order Statisticsin Impulsive Noise. IEEE\/CAA J. Autom. Sin., 1\u20139."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1547","DOI":"10.1016\/j.sigpro.2006.12.015","article-title":"Robust subspace-based algorithms for joint angle\/Doppler estimation in non-Gaussian clutter","volume":"87","author":"Belkacemi","year":"2007","journal-title":"Signal Process."},{"key":"ref_30","first-page":"34","article-title":"A new DOA algorithm based on nonlinear compress core Function in symmetric \u03b1-stable distribution noise environment","volume":"54","author":"Ma","year":"2014","journal-title":"Telecommun. Eng."},{"key":"ref_31","unstructured":"Ma, J.Q., Ge, L.D., and Tong, L. (2013, January 12\u201315). A TDE method based on nonlinear compress core function for HF fading signal in impulsive noise. Proceedings of the 8th International Conference on Broadband Communications & Biomedical Applications, Guilin, China."},{"key":"ref_32","first-page":"5","article-title":"A method for two dimensional parameters estimation of near-field sources in impulsive noise environments","volume":"10","author":"Wang","year":"2005","journal-title":"J. Circuits Syst."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"4030","DOI":"10.1007\/s00034-015-0234-y","article-title":"A Novel Method for Near-Field Source Localization in Impulsive Noise Environments","volume":"35","author":"Qiu","year":"2016","journal-title":"Circuits Syst. Signal Process."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Li, S., Lin, B., Li, B., and He, R.X. (2017, January 19\u201321). Near-Field Localization Algorithm Based on Sparse Reconstruction of the Fractional Lower Order Correlation Vector. Proceedings of the International Conference on Wireless Algorithms, Systems, and Applications, Guilin, China.","DOI":"10.1007\/978-3-319-60033-8_79"},{"key":"ref_35","unstructured":"Grant, M., Boyd, S., and Ye, Y. (CVX: Matlab Software for Disciplined Convex Programming, 2008). CVX: Matlab Software for Disciplined Convex Programming."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/4\/1066\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T14:59:22Z","timestamp":1760194762000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/4\/1066"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,4,2]]},"references-count":35,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2018,4]]}},"alternative-id":["s18041066"],"URL":"https:\/\/doi.org\/10.3390\/s18041066","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2018,4,2]]}}}