{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,14]],"date-time":"2025-10-14T00:33:20Z","timestamp":1760402000639,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2020,1,27]],"date-time":"2020-01-27T00:00:00Z","timestamp":1580083200000},"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":["61473197","11871357"],"award-info":[{"award-number":["61473197","11871357"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Sichuan Science and Technology Program","award":["2019YJ0115"],"award-info":[{"award-number":["2019YJ0115"]}]},{"DOI":"10.13039\/501100018621","name":"Program for Changjiang Scholars and Innovative Research Team in University","doi-asserted-by":"publisher","award":["IRT 16R53"],"award-info":[{"award-number":["IRT 16R53"]}],"id":[{"id":"10.13039\/501100018621","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This paper considers the binary Gaussian distribution robust hypothesis testing under a Bayesian optimal criterion in the wireless sensor network (WSN). The distribution covariance matrix under each hypothesis is known, while the distribution mean vector under each hypothesis drifts in an ellipsoidal uncertainty set. Because of the limited bandwidth and energy, we aim at seeking a subset of p out of m sensors such that the best detection performance is achieved. In this setup, the minimax robust sensor selection problem is proposed to deal with the uncertainties of distribution means. Following a popular method, minimizing the maximum overall error probability with respect to the selection matrix can be approximated by maximizing the minimum Chernoff distance between the distributions of the selected measurements under null hypothesis and alternative hypothesis to be detected. Then, we utilize Danskin\u2019s theorem to compute the gradient of the objective function of the converted maximization problem, and apply the orthogonal constraint-preserving gradient algorithm (OCPGA) to solve the relaxed maximization problem without 0\/1 constraints. It is shown that the OCPGA can obtain a stationary point of the relaxed problem. Meanwhile, we provide the computational complexity of the OCPGA, which is much lower than that of the existing greedy algorithm. Finally, numerical simulations illustrate that, after the same projection and refinement phases, the OCPGA-based method can obtain better solutions than the greedy algorithm-based method but with up to     48.72 %     shorter runtimes. Particularly, for small-scale problems, the OCPGA -based method is able to attain the globally optimal solution.<\/jats:p>","DOI":"10.3390\/s20030697","type":"journal-article","created":{"date-parts":[[2020,1,27]],"date-time":"2020-01-27T11:41:57Z","timestamp":1580125317000},"page":"697","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Gradient-Based Method for Robust Sensor Selection in Hypothesis Testing"],"prefix":"10.3390","volume":"20","author":[{"given":"Ting","family":"Ma","sequence":"first","affiliation":[{"name":"College of Mathematics, Sichuan University, Chengdu 610064, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bo","family":"Qian","sequence":"additional","affiliation":[{"name":"School of Electronic Science and Engineering, Nanjing University, Nanjing 210023, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dunbiao","family":"Niu","sequence":"additional","affiliation":[{"name":"College of Mathematics, Sichuan University, Chengdu 610064, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Enbin","family":"Song","sequence":"additional","affiliation":[{"name":"College of Mathematics, Sichuan University, Chengdu 610064, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qingjiang","family":"Shi","sequence":"additional","affiliation":[{"name":"School of Software Engineering, Tongji University, Shanghai 201804, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,1,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Gerla, M., Lee, E.K., Pau, G., and Lee, U. (2014, January 6\u20138). Internet of vehicles: From intelligent grid to autonomous cars and vehicular clouds. Proceedings of the IEEE World Forum on Internet of Things, Seoul, Korea.","DOI":"10.1109\/WF-IoT.2014.6803166"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Bahrepour, M., Meratnia, N., Poel, M., Taghikhaki, Z., and Havinga, P.J. (2010, January 24\u201326). Distributed event detection in wireless sensor networks for disaster management. Proceedings of the IEEE International Conference on Intelligent Networking and Collaborative Systems, Thessaloniki, Greece.","DOI":"10.1109\/INCOS.2010.24"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Rowaihy, H., Eswaran, S., Johnson, M., Verma, D., Bar-Noy, A., Brown, T., and La Porta, T. (2007, January 11). A survey of sensor selection schemes in wireless sensor networks. Proceedings of the Unattended Ground, Sea, and Air Sensor Technologies and Applications IX, Orlando, FL, USA.","DOI":"10.1117\/12.723514"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Guy, C. (2006, January 24). Wireless sensor networks. Proceedings of the Sixth International Symposium on Instrumentation and Control Technology: Signal Analysis, Measurement Theory, Photo-Electronic Technology, and Artificial Intelligence, Beijing, China.","DOI":"10.1117\/12.716964"},{"key":"ref_5","first-page":"415","article-title":"Power optimization in wireless sensor networks","volume":"8","author":"Bhattacharya","year":"2011","journal-title":"Int. J. Comput. Sci. Issues"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Weimer, J.E., Sinopoli, B., and Krogh, B.H. (2008, January 17\u201320). A relaxation approach to dynamic sensor selection in large-scale wireless networks. Proceedings of the IEEE International Conference on Distributed Computing Systems Workshops, Beijing, China.","DOI":"10.1109\/ICDCS.Workshops.2008.82"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1109\/TSP.2013.2289881","article-title":"Sensor selection based on generalized information gain for target tracking in large sensor networks","volume":"62","author":"Shen","year":"2013","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2092","DOI":"10.1016\/j.microrel.2015.06.076","article-title":"Entropy-based sensor selection for condition monitoring and prognostics of aircraft engine","volume":"55","author":"Liu","year":"2015","journal-title":"Microelectron. Reliab."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Bajovic, D., Sinopoli, B., and Xavier, J. (2009, January 15\u201318). Sensor selection for hypothesis testing in wireless sensor networks: A Kullback-Leibler based approach. Proceedings of the 48th IEEE Conference on Decision Control, Shanghai, China.","DOI":"10.1109\/CDC.2009.5400743"},{"key":"ref_10","unstructured":"Bajovic, D., Sinopoli, B., and Xavier, J. (October, January 30). Robust linear dimensionality reduction for hypothesis testing with application to sensor selection. Proceedings of the 47th Annual Allerton Conference on Communication, Control, and Computing, Monticello, IL, USA."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"4938","DOI":"10.1109\/TSP.2011.2160630","article-title":"Sensor selection for event detection in wireless sensor networks","volume":"59","author":"Bajovic","year":"2011","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"684","DOI":"10.1109\/TSP.2014.2379662","article-title":"Sparsity-promoting sensor selection for non-linear measurement models","volume":"63","author":"Chepuri","year":"2015","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"3687","DOI":"10.1109\/TSP.2015.2425804","article-title":"A stochastic sensor selection scheme for sequential hypothesis testing with multiple sensors","volume":"63","author":"Bai","year":"2015","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1007\/s10107-012-0584-1","article-title":"A feasible method for optimization with orthogonality constraints","volume":"142","author":"Wen","year":"2013","journal-title":"Math. Program."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1163","DOI":"10.1016\/0362-546X(94)00186-L","article-title":"On a theorem of Danskin with an application to a theorem of Von Neumann-Sion","volume":"24","author":"Bernhard","year":"1995","journal-title":"Nonlinear Anal."},{"key":"ref_16","unstructured":"Scharf, L.L. (1991). Statistical Signal Processing: Detection, Estimation and Time Series Analysis, Addison-Wesley Publishing Company."},{"key":"ref_17","unstructured":"Cover, T.M., and Thomas, J.A. (1991). Elements of Information Theory, Wiley."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"156","DOI":"10.1007\/s11263-008-0193-x","article-title":"Cayley transformation and numerical stability of Calibration equation","volume":"82","author":"Wu","year":"2009","journal-title":"Int. J. Comput. Vis."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1137\/080726926","article-title":"A curvilinear search method for p-harmonic flows on spheres","volume":"2","author":"Goldfarb","year":"2009","journal-title":"SIAM J. Imaging Sci."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1093\/imanum\/8.1.141","article-title":"Two-point step size gradient methods","volume":"8","author":"Barzilai","year":"1988","journal-title":"IMA J. Numer. Anal."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1043","DOI":"10.1137\/S1052623403428208","article-title":"A nonmonotone line search technique and its application to unconstrained optimization","volume":"14","author":"Zhang","year":"2004","journal-title":"SIAM J. Optim."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"302","DOI":"10.1137\/16M1098759","article-title":"A new first-order framework for orthogonal constrained optimization problems","volume":"28","author":"Gao","year":"2018","journal-title":"SIAM J. Optim."},{"key":"ref_23","unstructured":"Xia, D.X., Shu, W.C., Yan, S.Z., and Tong, Y.S. (1986). Second Course for Functional Analysis, Higher Education Press."},{"key":"ref_24","unstructured":"Bonnans, J.F., and Shapiro, A. (2013). Perturbation Analysis of Optimization Problems, Springer Science & Business Media."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Ricceri, B., and Simons, S. (1998). Minimax Theory and Applications, Kluwer Academic Pub.","DOI":"10.1007\/978-94-015-9113-3"},{"key":"ref_26","unstructured":"Grant, M., Boyd, S., and Ye, Y. (2009). CVX Toolbox, Stanford University Press."},{"key":"ref_27","unstructured":"Nemirovskii, A., and Nesterov, Y. (1994). Interior-Point Polynomial Algorithms in Convex Programming, SIAM."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Boyd, S., and Vandenberghe, L. (2004). Convex Optimization, Cambridge University Press.","DOI":"10.1017\/CBO9780511804441"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Ekeland, I., and Temam, R. (1999). Convex Analysis and Variational Problems, SIAM.","DOI":"10.1137\/1.9781611971088"},{"key":"ref_30","unstructured":"Clarke, F.H. (1978, January 15\u201323). Nonsmooth analysis and optimization. Proceedings of the International Congress of Mathematicians, Helsinki, Finland."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/3\/697\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T13:20:44Z","timestamp":1760361644000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/3\/697"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,1,27]]},"references-count":30,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2020,2]]}},"alternative-id":["s20030697"],"URL":"https:\/\/doi.org\/10.3390\/s20030697","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2020,1,27]]}}}