{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T14:11:44Z","timestamp":1760191904338,"version":"build-2065373602"},"reference-count":63,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2019,12,21]],"date-time":"2019-12-21T00:00:00Z","timestamp":1576886400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61902068","61972092","61401496"],"award-info":[{"award-number":["61902068","61972092","61401496"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Major Natural Science Research of the Anhui Higher Education Institution of China","award":["KJ2019ZD44"],"award-info":[{"award-number":["KJ2019ZD44"]}]},{"name":"Foshan Self-found S&amp;T Innovation Plan","award":["1920001001001"],"award-info":[{"award-number":["1920001001001"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>We propose a sparsity-aware noise subspace fitting (SANSF) algorithm for direction-of-arrival (DOA) estimation using an array of sensors. The proposed SANSF algorithm is developed from the optimally weighted noise subspace fitting criterion. Our formulation leads to a convex linearly constrained quadratic programming (LCQP) problem that enjoys global convergence without the need of accurate initialization and can be easily solved by existing LCQP solvers. Combining the weighted quadratic objective function, the     \u2113 1     norm, and the non-negative constraints, the proposed SANSF algorithm can enhance the sparsity of the solution. Numerical results based on simulations, using real measured ultrasonic, and radar data, show that, compared to existing sparsity-aware methods, the proposed SANSF can provide enhanced resolution with a lower computational burden.<\/jats:p>","DOI":"10.3390\/s20010081","type":"journal-article","created":{"date-parts":[[2019,12,23]],"date-time":"2019-12-23T03:15:01Z","timestamp":1577070901000},"page":"81","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Sparsity-Aware Noise Subspace Fitting for DOA Estimation"],"prefix":"10.3390","volume":"20","author":[{"given":"Chundi","family":"Zheng","sequence":"first","affiliation":[{"name":"School of Electronic Information Engineering, Foshan University, Foshan 528231, Guangdong, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huihui","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Electronic Information Engineering, Foshan University, Foshan 528231, Guangdong, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Aiguo","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Electronic Information Engineering, Foshan University, Foshan 528231, Guangdong, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,12,21]]},"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: The parametric approach","volume":"13","author":"Krim","year":"1996","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_2","unstructured":"Athanassios, M. (2015). Beamforming: Sensor Signal Processing for Defence Applications, Imperial College Press."},{"key":"ref_3","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_4","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_5","doi-asserted-by":"crossref","first-page":"1132","DOI":"10.1109\/29.57542","article-title":"Maximum likelihood methods for direction-of-arrival estimation","volume":"38","author":"Stoica","year":"1990","journal-title":"IEEE Trans. Acoust. Speech Signal Process."},{"key":"ref_6","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_7","doi-asserted-by":"crossref","first-page":"2477","DOI":"10.1109\/TSP.2005.849172","article-title":"Sparse solutions to linear inverse problems with multiple measurement vectors","volume":"53","author":"Cotter","year":"2005","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_8","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_9","doi-asserted-by":"crossref","first-page":"629","DOI":"10.1109\/TSP.2010.2090525","article-title":"SPICE: A sparse covariance-based estimation method for array processing","volume":"59","author":"Stoica","year":"2011","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"4489","DOI":"10.1109\/TSP.2011.2158425","article-title":"Direction-of-arrival estimation using a sparse representation of array covariance vectors","volume":"59","author":"Yin","year":"2011","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1109\/LSP.2012.2183592","article-title":"DOA Estimation Based on Sparse Signal Recovery Utilizing Weighted \u21131 norm penalty","volume":"19","author":"Xu","year":"2012","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_12","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 Process. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Fan, Y., Wang, J., Du, R., and Lv, G. (2018). Sparse method for direction of arrival estimation using denoised fourth-order cumulants vector. Sensors, 18.","DOI":"10.3390\/s18061815"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"8549","DOI":"10.1109\/TVT.2018.2851783","article-title":"Deep learning for super-resolution channel estimation and DOA estimation based massive MIMO system","volume":"67","author":"Huang","year":"2018","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1783","DOI":"10.1109\/29.60109","article-title":"Performance study of conditional and unconditional direction-of-arrival estimation","volume":"38","author":"Stoica","year":"1990","journal-title":"IEEE Trans. Acoust. Speech Signal Process."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Ottersten, B., Viberg, M., Stoica, P., and Nehorai, A. (1993). Exact and Large Sample Maximum Likelihood Techniques for Parameter Estimation and Detection in Array Processing. Radar Array Processing, Springer.","DOI":"10.1007\/978-3-642-77347-1_4"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1109\/78.482015","article-title":"Maximum likelihood array processing for stochastic coherent sources","volume":"44","author":"Stoica","year":"1996","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1109\/5.659495","article-title":"Maximum likelihood methods in radar array signal processing","volume":"86","author":"Swindlehurst","year":"1998","journal-title":"Proc. IEEE"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1109\/TAES.2017.2756519","article-title":"Digital monopulse beamforming for achieving the CRLB for angle accuracy","volume":"54","author":"Takahashi","year":"2018","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1553","DOI":"10.1109\/29.7543","article-title":"Maximum likelihood localization of multiple sources by alternating projection","volume":"36","author":"Ziskind","year":"1988","journal-title":"IEEE Trans. Acoust. Speech Signal Process."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1049\/ip-f-2.1990.0004","article-title":"Novel eigenanalysis method for direction estimation","volume":"137","author":"Stoica","year":"1990","journal-title":"IEE Proc. F (Radar Signal Process.)"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1109\/78.651203","article-title":"Comparative study of IQML and MODE direction-of-arrival estimators","volume":"46","author":"Li","year":"1998","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_23","unstructured":"Zheng, C., Li, G., Zhang, H., and Wang, X. (2011, January 22\u201327). An approach of DOA estimation using noise subspace weighted \u21131 minimization. Proceedings of the 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Prague, Czech Republic."},{"key":"ref_24","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":"2012","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_25","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_26","doi-asserted-by":"crossref","unstructured":"Si, W., Zeng, F., Hou, C., and Peng, Z. (2018). A sparse-based off-grid DOA estimation method for coprime arrays. Sensors, 18.","DOI":"10.3390\/s18093025"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"702","DOI":"10.1109\/78.912914","article-title":"On the application of the global matched filter to DOA estimation with uniform circular arrays","volume":"49","author":"Fuchs","year":"2001","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_28","unstructured":"Fuchs, J.J. (2009, January 24\u201328). DOA estimation in the presence of modeling errors, the global matched filter approach. Proceedings of the 17th European Signal Processing Conference (EUSIPCO), Glasgow, UK."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Nesterov, Y., Nemirovskii, A., and Ye, Y. (1994). Interior-Point Polynomial Algorithms in Convex Programming, SIAM.","DOI":"10.1137\/1.9781611970791"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1580","DOI":"10.1016\/j.sigpro.2011.11.010","article-title":"SPICE and LIKES: Two hyperparameter-free methods for sparse-parameter estimation","volume":"92","author":"Stoica","year":"2012","journal-title":"Signal Process."},{"key":"ref_31","unstructured":"Babu, P., and Stoica, P. (2012, January 27\u201331). Sparse spectral-line estimation for nonuniformly sampled multivariate time series: SPICE, LIKES and MSBL. Proceedings of the 20th European Signal Processing Conference (EUSIPCO), Bucharest, Romania."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Yang, Z., and Xie, L. (2016, January 20\u201325). On gridless sparse methods for multi-snapshot DOA estimation. Proceedings of the 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Shanghai, China.","DOI":"10.1109\/ICASSP.2016.7472275"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"3370","DOI":"10.1007\/s00034-016-0462-9","article-title":"On gridless sparse methods for multi-snapshot direction of arrival estimation","volume":"36","author":"Yang","year":"2017","journal-title":"Circuits Syst. Signal Process."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1845","DOI":"10.1109\/LCOMM.2019.2929384","article-title":"A novel block sparse reconstruction method for DOA estimation with unknown mutual coupling","volume":"23","author":"Zhang","year":"2019","journal-title":"IEEE Commun. Lett."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1007\/s12532-014-0071-1","article-title":"qpOASES: A parametric active-set algorithm for quadratic programming","volume":"6","author":"Ferreau","year":"2014","journal-title":"Math. Program. Comput."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Pougkakiotis, S., and Gondzio, J. (2019). An Interior Point-Proximal Method of Multipliers for Convex Quadratic Programming. arXiv.","DOI":"10.1007\/s10589-020-00240-9"},{"key":"ref_37","unstructured":"Nocedal, J., and Wright, S. (2006). Numerical Optimization, Springer Science & Business Media."},{"key":"ref_38","first-page":"1","article-title":"Numerical shape-from-shading revisited","volume":"10","author":"Santo","year":"2018","journal-title":"IPSJ Trans. Comput. Vis. Appl."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"416","DOI":"10.1214\/aos\/1176346150","article-title":"A universal prior for integers and estimation by minimum description length","volume":"11","author":"Rissanen","year":"1983","journal-title":"Ann. Stat."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"2809","DOI":"10.1137\/17M1128538","article-title":"A two-phase gradient method for quadratic programming problems with a single linear constraint and bounds on the variables","volume":"28","author":"Toraldo","year":"2018","journal-title":"SIAM J. Optim."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1109\/LCOMM.2013.111413.131722","article-title":"Denoising detection for the generalized spatial modulation system using sparse property","volume":"18","author":"Liu","year":"2014","journal-title":"IEEE Commun. Lett."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1049\/ip-rsn:19941366","article-title":"Alternative algorithm for maximum likelihood DOA estimation and detection","volume":"141","author":"Swindlehurst","year":"1994","journal-title":"IEE Proc. Radar Sonar Navig."},{"key":"ref_43","unstructured":"Horn, R.A., and Johnson, C.R. (1990). Matrix Analysis, Cambridge University Press."},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Horn, R.A., and Johnson, C.R. (1991). Topics in Matrix Analysis, Cambridge University Press.","DOI":"10.1017\/CBO9780511840371"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1170","DOI":"10.1109\/7.259520","article-title":"Performance analysis for DOA estimation algorithms: Unification, simplification, and observations","volume":"29","author":"Li","year":"1993","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"877","DOI":"10.1007\/s00041-008-9045-x","article-title":"Enhancing sparsity by reweighted \u21131 minimization","volume":"14","author":"Candes","year":"2008","journal-title":"J. Fourier Anal. Appl."},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Xu, W., Khajehnejad, M., Avestimehr, A., and Hassibi, B. (2010, January 14\u201319). Breaking through the thresholds: An analysis for iterative reweighted \u21131 minimization via the Grassmann angle framework. Proceedings of the 2010 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP ), Dallas, TX, USA.","DOI":"10.1109\/ICASSP.2010.5495210"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"98","DOI":"10.1186\/1687-6180-2012-98","article-title":"Subspace weighted \u21132,1, minimization for sparse signal recovery","volume":"2012","author":"Zheng","year":"2012","journal-title":"EURASIP Eurasip J. Adv. Signal Process."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1109\/JSTSP.2010.2042413","article-title":"Iterative reweighted \u21131 and \u21132 methods for finding sparse solutions","volume":"4","author":"Wipf","year":"2010","journal-title":"IEEE J. Sel. Top. Signal Process."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1016\/j.sigpro.2013.10.009","article-title":"Robust adaptive beamforming based on interference covariance matrix sparse reconstruction","volume":"96","author":"Gu","year":"2014","journal-title":"Signal Process."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"3004","DOI":"10.1214\/13-EJS868","article-title":"Non-negative least squares for high-dimensional linear models: Consistency and sparse recovery without regularization","volume":"7","author":"Slawski","year":"2013","journal-title":"Electron. J. Stat."},{"key":"ref_52","doi-asserted-by":"crossref","unstructured":"Eftekhari, A., Tanner, J., Thompson, A., Toader, B., and Tyagi, H. (2019). Sparse non-negative super-resolution\u2014simplified and stabilised. Appl. Comput. Harmon. Anal.","DOI":"10.1109\/DSW.2018.8439120"},{"key":"ref_53","doi-asserted-by":"crossref","unstructured":"Kou, J., Li, M., and Jiang, C. (2019). A Robust DOA Estimator Based on Compressive Sensing for Coprime Array in the Presence of Miscalibrated Sensors. Sensors, 19.","DOI":"10.3390\/s19163538"},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"2559","DOI":"10.1109\/78.157296","article-title":"Bias analysis of the MUSIC location estimator","volume":"40","author":"Xu","year":"1992","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"2748","DOI":"10.1109\/TSP.2005.850361","article-title":"Capon algorithm mean-squared error threshold SNR prediction and probability of resolution","volume":"53","author":"Richmond","year":"2005","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_56","unstructured":"Johnson, D., and Dudgeon, D. (1993). Array Signal Processing: Concepts and Techniques, Prentice-Hall."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"725","DOI":"10.1109\/JOE.2017.2706100","article-title":"Comparison of Two Hyperparameter-Free Sparse Signal Processing Methods for Direction-of-Arrival Tracking in the HF97 Ocean Acoustic Experiment","volume":"43","author":"Das","year":"2018","journal-title":"IEEE J. Ocean. Eng."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"978","DOI":"10.1109\/78.376849","article-title":"Probability of resolution of the MUSIC algorithm","volume":"43","author":"Zhang","year":"1995","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_59","unstructured":"Stoica, P., and Moses, R. (2005). Spectral Analysis of Signals, Pearson\/Prentice Hall."},{"key":"ref_60","unstructured":"Pierre, J.W., Scott, E.D., and Hays, M.P. (1997, January 21\u201324). A sensor array testbed for source tracking algorithms. Proceedings of the 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Munich, Germany."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0165-1684(98)00130-3","article-title":"A pseudo-noise approach to direction finding","volume":"71","author":"Gershman","year":"1998","journal-title":"Signal Process."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1006\/dspr.1999.0332","article-title":"On Unitary and Forward-Backward MODE","volume":"9","author":"Gershman","year":"1999","journal-title":"Digit. Signal Process."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"859","DOI":"10.1109\/TAP.2010.2103015","article-title":"Through-wall opportunistic sensing system utilizing a low-cost flat-panel array","volume":"59","author":"Browne","year":"2011","journal-title":"IEEE Trans. Antennas Propag."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/1\/81\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:44:32Z","timestamp":1760190272000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/1\/81"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,12,21]]},"references-count":63,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2020,1]]}},"alternative-id":["s20010081"],"URL":"https:\/\/doi.org\/10.3390\/s20010081","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2019,12,21]]}}}