{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,17]],"date-time":"2026-04-17T04:57:08Z","timestamp":1776401828299,"version":"3.51.2"},"reference-count":32,"publisher":"MDPI AG","issue":"16","license":[{"start":{"date-parts":[[2019,8,13]],"date-time":"2019-08-13T00:00:00Z","timestamp":1565654400000},"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>Coprime array with     M + N     sensors can achieve an increased degrees-of-freedom (DOF) of     O  (  M N  )      for direction-of-arrival (DOA) estimation. Utilizing the compressive sensing (CS)-based DOA estimation methods, the increased DOF offered by the coprime array can be fully exploited. However, when some sensors in the array are miscalibrated, these DOA estimation methods suffer from degraded performance or even failed operation. Besides, the key to the success of CS-based DOA estimation is that every target falls on the predefined grid. Thus, a coarse grid may cause the mismatch problem, whereas a fine grid requires great computational cost. In this paper, a robust CS-based DOA estimation algorithm is proposed for coprime array with miscalibrated sensors. In the proposed algorithm, signals received by the miscalibrated sensors are viewed as outliers, and correntropy is introduced as the similarity measurement to distinguish these outliers. Incorporated with maximum correntropy criterion (MCC), an iterative sparse reconstruction-based algorithm is then developed to give the DOA estimation while mitigating the influence of the outliers. A multiresolution grid refinement strategy is also incorporated to reconcile the contradiction between computational cost and the mismatch problem. The numerical simulation results verify the effectiveness and robustness of the proposed method.<\/jats:p>","DOI":"10.3390\/s19163538","type":"journal-article","created":{"date-parts":[[2019,8,14]],"date-time":"2019-08-14T03:59:26Z","timestamp":1565755166000},"page":"3538","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["A Robust DOA Estimator Based on Compressive Sensing for Coprime Array in the Presence of Miscalibrated Sensors"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2996-5098","authenticated-orcid":false,"given":"Jiaxun","family":"Kou","sequence":"first","affiliation":[{"name":"State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ming","family":"Li","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chunlan","family":"Jiang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,8,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1109\/79.526899","article-title":"Two decades of array signal processing research\u2014The parametric approach","volume":"13","author":"Krim","year":"1996","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_2","unstructured":"Trees, H.L.V. (2004). Detection, Estimation, and Modulation Theory, Part IV: Optimum Array Processing, Wiley."},{"key":"ref_3","unstructured":"Tuncer, T.E., and Friedlander, B. (2009). Practical aspects of design and application of direction-finding systems. Classical and Modern Direction-of-Arrival Estimation, Academic Press."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"573","DOI":"10.1109\/TSP.2010.2089682","article-title":"Sparse sensing with co-prime samplers and arrays","volume":"59","author":"Vaidyanathan","year":"2011","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Pal, P., and Vaidyanathan, P.P. (2011, January 4\u20137). Coprime sampling and the MUSIC algorithm. Proceedings of the 2011 IEEE Digital Signal Processing Workshop & IEEE Signal Processing Education Workshop (DSP\/SPE), Sedona, AZ, USA.","DOI":"10.1109\/DSP-SPE.2011.5739227"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1710","DOI":"10.1109\/LSP.2018.2872400","article-title":"Off-grid direction-of-arrival estimation using coprime array interpolation","volume":"25","author":"Zhou","year":"2018","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Zhang, Y.D., Amin, M.G., and Himed, B. (2013, January 26\u201331). Sparsity-based DOA estimation using co-prime arrays. Proceedings of the 2013 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Vancouver, BC, Canada.","DOI":"10.1109\/ICASSP.2013.6638403"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1289","DOI":"10.1109\/TIT.2006.871582","article-title":"Compressed sensing","volume":"52","author":"Donoho","year":"2006","journal-title":"IEEE Trans. Inf. Theory."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"4655","DOI":"10.1109\/TIT.2007.909108","article-title":"Signal recovery from random measurements via orthogonal matching pursuit","volume":"53","author":"Tropp","year":"2007","journal-title":"IEEE Trans. Inf. Theory."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1111\/j.2517-6161.1996.tb02080.x","article-title":"Regression shrinkage and selection via the lasso","volume":"58","author":"Tibshirani","year":"1996","journal-title":"J. R. Stat. Soc. Ser. B. Stat. Methodol."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"4133","DOI":"10.1109\/TSP.2018.2847645","article-title":"DOA estimation using compressed sparse array","volume":"66","author":"Guo","year":"2018","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"5944","DOI":"10.1109\/TSP.2011.2165064","article-title":"An eigenstructure method for estimating DOA and sensor gain-phase errors","volume":"59","author":"Liu","year":"2011","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_13","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_14","doi-asserted-by":"crossref","first-page":"922","DOI":"10.1109\/TAP.2011.2173144","article-title":"Direction finding with partly calibrated uniform linear arrays","volume":"60","author":"Liao","year":"2012","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1346","DOI":"10.1049\/iet-rsn.2018.5087","article-title":"DOA estimation based on compressed sensing with gain\/phase uncertainties","volume":"12","author":"Hu","year":"2018","journal-title":"IET Radar Sonar Navig."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1016\/j.dsp.2018.10.005","article-title":"Sparsity based off-grid blind sensor calibration","volume":"84","author":"Camlica","year":"2019","journal-title":"Digit. Signal Prog."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"6018","DOI":"10.1109\/JSEN.2016.2577712","article-title":"A sparse-based approach for DOA estimation and array calibration in uniform linear array","volume":"16","author":"Liu","year":"2016","journal-title":"IEEE Sens. J."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"4847","DOI":"10.1109\/TSP.2014.2342651","article-title":"Convex optimization approaches for blind sensor calibration using sparsity","volume":"62","author":"Bilen","year":"2014","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"65367","DOI":"10.1109\/ACCESS.2018.2878152","article-title":"Direction of arrival estimation by convex optimization methods with unknown sensor gain and phase","volume":"6","author":"Liu","year":"2018","journal-title":"IEEE Access"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1017\/S1759078718001575","article-title":"An improved gain-phase error self-calibration method for robust DOA estimation","volume":"11","author":"Peng","year":"2019","journal-title":"Int. J. Microw. Wirel. Technol."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"54514","DOI":"10.1109\/ACCESS.2018.2873416","article-title":"Direction-of-arrival estimation via coarray with model errors","volume":"6","author":"Lu","year":"2018","journal-title":"IEEE Access"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1073","DOI":"10.1109\/LSP.2017.2708659","article-title":"Robust DOA estimation in the presence of miscalibrated sensors","volume":"24","author":"Wang","year":"2017","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1438","DOI":"10.1109\/LSP.2015.2409153","article-title":"Remarks on the spatial smoothing step in coarray MUSIC","volume":"22","author":"Liu","year":"2015","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"66","DOI":"10.1016\/j.dsp.2018.04.003","article-title":"Coprime array-based DOA estimation in unknown nonuniform noise environment","volume":"79","author":"Liu","year":"2018","journal-title":"Digit. Signal Prog."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"5286","DOI":"10.1109\/TSP.2007.896065","article-title":"Correntropy: Properties and applications in non-gaussian signal processing","volume":"55","author":"Liu","year":"2007","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Yuan, X., and Hu, B.G. (2009, January 14\u201318). Robust feature extraction via information theoretic learning. Proceedings of the 2009 International Conference on Machine Learning, Montreal, QC, Canada.","DOI":"10.1145\/1553374.1553526"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Rockafellar, R.T. (1970). Convex analysis, Princeton University Press.","DOI":"10.1515\/9781400873173"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/j.sigpro.2015.11.004","article-title":"Robust MIMO radar target localization via nonconvex optimization","volume":"122","author":"Liang","year":"2016","journal-title":"Signal Process."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"3010","DOI":"10.1109\/TSP.2005.850882","article-title":"A sparse signal reconstruction perspective for source localization with sensor arrays","volume":"53","author":"Malioutov","year":"2005","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1016\/j.dsp.2016.04.011","article-title":"Cramer-Rao bounds for coprime and other sparse arrays, which find more sources than sensors","volume":"61","author":"Liu","year":"2017","journal-title":"Digit. Signal Prog."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Liu, C.L., Vaidyanathan, P.P., and Pal, P. (2016, January 22\u201325). Coprime coarray interpolation for DOA estimation via nuclear norm minimization. Proceedings of the 2016 IEEE International Symposium on Circuits & Systems (ISCAS), Montreal, QC, Canada.","DOI":"10.1109\/ISCAS.2016.7539135"},{"key":"ref_32","unstructured":"Grant, M., and Boyd, S. (2014, March 31). CVX: Matlab Software for Disciplined Convex Programming, Version 2.1. Available online: http:\/\/cvxr.com\/cvx."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/16\/3538\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:10:47Z","timestamp":1760188247000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/16\/3538"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,8,13]]},"references-count":32,"journal-issue":{"issue":"16","published-online":{"date-parts":[[2019,8]]}},"alternative-id":["s19163538"],"URL":"https:\/\/doi.org\/10.3390\/s19163538","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,8,13]]}}}