{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,17]],"date-time":"2026-04-17T15:52:46Z","timestamp":1776441166882,"version":"3.51.2"},"reference-count":50,"publisher":"MDPI AG","issue":"15","license":[{"start":{"date-parts":[[2022,7,28]],"date-time":"2022-07-28T00:00:00Z","timestamp":1658966400000},"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":["62007022"],"award-info":[{"award-number":["62007022"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61906146"],"award-info":[{"award-number":["61906146"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["2021JQ-209"],"award-info":[{"award-number":["2021JQ-209"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["GK202103082"],"award-info":[{"award-number":["GK202103082"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["JB210210"],"award-info":[{"award-number":["JB210210"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007128","name":"Natural Science Foundation of Shaanxi Province","doi-asserted-by":"publisher","award":["62007022"],"award-info":[{"award-number":["62007022"]}],"id":[{"id":"10.13039\/501100007128","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007128","name":"Natural Science Foundation of Shaanxi Province","doi-asserted-by":"publisher","award":["61906146"],"award-info":[{"award-number":["61906146"]}],"id":[{"id":"10.13039\/501100007128","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007128","name":"Natural Science Foundation of Shaanxi Province","doi-asserted-by":"publisher","award":["2021JQ-209"],"award-info":[{"award-number":["2021JQ-209"]}],"id":[{"id":"10.13039\/501100007128","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007128","name":"Natural Science Foundation of Shaanxi Province","doi-asserted-by":"publisher","award":["GK202103082"],"award-info":[{"award-number":["GK202103082"]}],"id":[{"id":"10.13039\/501100007128","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007128","name":"Natural Science Foundation of Shaanxi Province","doi-asserted-by":"publisher","award":["JB210210"],"award-info":[{"award-number":["JB210210"]}],"id":[{"id":"10.13039\/501100007128","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["62007022"],"award-info":[{"award-number":["62007022"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["61906146"],"award-info":[{"award-number":["61906146"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["2021JQ-209"],"award-info":[{"award-number":["2021JQ-209"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["GK202103082"],"award-info":[{"award-number":["GK202103082"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["JB210210"],"award-info":[{"award-number":["JB210210"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>In multi-sensor systems (MSSs), sensor selection is a critical technique for obtaining high-quality sensing data. However, when the number of sensors to be selected is unknown in advance, sensor selection is essentially non-deterministic polynomial-hard (NP-hard), and finding the optimal solution is computationally unacceptable. To alleviate these issues, we propose a novel sensor selection approach based on evolutionary computational intelligence for tracking multiple targets in the MSSs. The sensor selection problem is formulated in a partially observed Markov decision process framework by modeling multi-target states as labeled multi-Bernoulli random finite sets. Two conflicting task-driven objectives are considered: minimization of the uncertainty in posterior cardinality estimates and minimization of the number of selected sensors. By modeling sensor selection as a multi-objective optimization problem, we develop a binary constrained evolutionary multi-objective algorithm based on non-dominating sorting and dynamically select a subset of sensors at each time step. Numerical studies are used to evaluate the performance of the proposed approach, where the MSS tracks multiple moving targets with nonlinear\/linear dynamic models and nonlinear measurements. The results show that our method not only significantly reduces the number of selected sensors but also provides superior tracking accuracy compared to generic sensor selection methods.<\/jats:p>","DOI":"10.3390\/rs14153624","type":"journal-article","created":{"date-parts":[[2022,7,28]],"date-time":"2022-07-28T22:43:26Z","timestamp":1659048206000},"page":"3624","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Evolutionary Computational Intelligence-Based Multi-Objective Sensor Management for Multi-Target Tracking"],"prefix":"10.3390","volume":"14","author":[{"given":"Shuang","family":"Liang","sequence":"first","affiliation":[{"name":"Academy of Advanced Interdisciplinary Research, Xidian University, Xi\u2019an 710071, China"}]},{"given":"Yun","family":"Zhu","sequence":"additional","affiliation":[{"name":"School of Computer Science, Shaanxi Normal University, Xi\u2019an 710119, China"}]},{"given":"Hao","family":"Li","sequence":"additional","affiliation":[{"name":"School of Electronic Engineering, Xidian University, Xi\u2019an 710071, China"}]},{"given":"Junkun","family":"Yan","sequence":"additional","affiliation":[{"name":"National Laboratory of Radar Signal Processing, Xidian University, Xi\u2019an 710071, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,7,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Gao, J., Zhang, Q., Sun, H., and Wang, W. (2022). A Multi-Sensor Interacted Vehicle-Tracking Algorithm with Time-Varying Observation Error. Remote Sens., 14.","DOI":"10.3390\/rs14092176"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Memon, S.A., Ullah, I., Khan, U., and Song, T.L. (2022). Smoothing Linear Multi-Target Tracking Using Integrated Track Splitting Filter. Remote Sens., 14.","DOI":"10.3390\/rs14051289"},{"key":"ref_3","unstructured":"Mallick, M., Krishnamurthy, V., and Vo, B.N. (2012). Integrated Tracking, Classification, and Sensor Management: Theory and Applications, Wiley Press."},{"key":"ref_4","unstructured":"Bar-Shalom, Y., Willett, P., and Tian, X. (2011). Tracking and Data Fusion: A Handbook of Algorithms, YBS Publishing."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Mahler, R. (1998). Global Posterior Densities for Sensor Management. Acquisition, Tracking, and Pointing XII, SPIE.","DOI":"10.1117\/12.317518"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"843","DOI":"10.1109\/TAC.1979.1102177","article-title":"An Algorithm for Tracking Multiple Targets","volume":"24","author":"Reid","year":"1979","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_7","unstructured":"Bar-Shalom, Y. (1990). Issues in The Design of Practical Multitarget Tracking Algorithms. Multitarget-Multisensor Tracking: Advanced Applications, Artech House."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1109\/JOE.1983.1145560","article-title":"Sonar Tracking of Multiple Targets Using Joint Probabilistic Data Association","volume":"8","author":"Fortmann","year":"2003","journal-title":"IEEE J. Ocean. Eng."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Mahler, R. (2007). Statistical Multisource-Multitarget Information Fusion, Artech House.","DOI":"10.1201\/9781420053098.ch16"},{"key":"ref_10","unstructured":"Mahler, R. (2014). Advances in Statistical Multisource-Multitarget Information Fusion, Artech House."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1152","DOI":"10.1109\/TAES.2003.1261119","article-title":"Multitarget Bayes Filtering via First-order Multitarget Moments","volume":"39","author":"Mahler","year":"2003","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1523","DOI":"10.1109\/TAES.2007.4441756","article-title":"PHD Filters of Higher Order in Target Number","volume":"43","author":"Mahler","year":"2007","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1109\/TSP.2008.2007924","article-title":"The Cardinality Balanced Multi-Target Multi-Bernoulli Filter and Its Implementations","volume":"57","author":"Vo","year":"2009","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"3460","DOI":"10.1109\/TSP.2013.2259822","article-title":"Labeled Random Finite Sets and Multi-Object Conjugate Priors","volume":"61","author":"Vo","year":"2013","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Vo, B.T., and Vo, B.N. (2011, January 6\u20139). A Random Finite Set Conjugate Prior and Application to Multi-target Tracking. Proceedings of the 2011 7th International Conference on Intelligent Sensors, Sensor Networks and Information Processing, Adelaide, SA, Australia.","DOI":"10.1109\/ISSNIP.2011.6146549"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"6554","DOI":"10.1109\/TSP.2014.2364014","article-title":"Labeled Random Finite Sets and the Bayes Multi-Target Tracking Filter","volume":"62","author":"Vo","year":"2014","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"3246","DOI":"10.1109\/TSP.2014.2323064","article-title":"The Labeled Multi-Bernoulli Filter","volume":"62","author":"Reuter","year":"2014","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Hero, A.O., Castanon, D., Cochran, D., and Kastella, K. (2008). Information Theoretic Approaches to Sensor Management. Foundations and Applications of Sensor Management, Springer. Chapter 3.","DOI":"10.1007\/978-0-387-49819-5"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1812","DOI":"10.1016\/j.automatica.2010.06.045","article-title":"Sensor Control for Multi-object State-space Estimation Using Random Finite Sets","volume":"46","author":"Ristic","year":"2010","journal-title":"Automatica"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"2078","DOI":"10.2514\/1.G004232","article-title":"Multisensor Tasking Using Analytical Renyi Divergence in Labeled Multi-Bernoulli Filtering","volume":"42","author":"Cai","year":"2019","journal-title":"J. Guid. Control Dyn."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"4475","DOI":"10.1109\/TIT.2015.2441709","article-title":"The Cauchy-Schwarz Divergence for Poisson Point Processes","volume":"61","author":"Hoang","year":"2015","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"5047","DOI":"10.1109\/TSP.2017.2723355","article-title":"Void Probabilities and Cauchy-Schwarz Divergence for Generalized Labeled Multi-Bernoulli Models","volume":"65","author":"Beard","year":"2017","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"2877","DOI":"10.1109\/TAES.2017.2718280","article-title":"Sensor-Management for Multitarget Filters via Minimization of Posterior Dispersion","volume":"53","author":"Gostar","year":"2017","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"5365","DOI":"10.1109\/TSP.2019.2939076","article-title":"Online UAV Path Planning for Joint Detection and Tracking of Multiple Radio-Tagged Objects","volume":"67","author":"Nguyen","year":"2019","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_25","unstructured":"Jiang, M., Yi, W., and Kong, L. (2016, January 5\u20138). Multi-sensor Control for Multi-target Tracking Using Cauchy-Schwarz Divergence. Proceedings of the 2016 19th International Conference on Information Fusion (FUSION), Heidelberg, Germany."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1135","DOI":"10.1016\/j.automatica.2014.02.007","article-title":"Sensor Management for Multi-target Tracking via Multi-Bernoulli Filtering","volume":"50","author":"Hoang","year":"2014","journal-title":"Automatica"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1762","DOI":"10.1109\/TAES.2015.140211","article-title":"Multi-Bernoulli Sensor Control via Minimization of Expected Estimation Errors","volume":"51","author":"Gostar","year":"2015","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Panicker, S., Gostar, A.K., Bab-Haidashar, A., and Hoseinnezhad, R. (2018, January 10\u201313). Sensor Control for Selective Object Tracking Using Labeled Multi-Bernoulli Filter. Proceedings of the 2018 21st International Conference on Information Fusion (FUSION), Cambridge, UK.","DOI":"10.23919\/ICIF.2018.8455829"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"107451","DOI":"10.1016\/j.sigpro.2019.107451","article-title":"Tracking of Targets of Interest Using Labeled Multi-Bernoulli Filter with Multi-Sensor Control","volume":"171","author":"Panicker","year":"2020","journal-title":"Signal Process."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Nguyen, H.V., Rezatofighi, H., Vo, B.N., and Ranasinghe, D. (2020, January 7\u201312). Multi-Objective Multi-Agent Planning for Jointly Discovering and Tracking Mobile Object. Proceedings of the AAAI Conference on Artificial Intelligence, New York, NY, USA.","DOI":"10.1609\/aaai.v34i05.6213"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Zhu, Y., Wang, J., and Liang, S. (2019). Multi-Objective Optimization Based Multi-Bernoulli Sensor Selection for Multi-Target Tracking. Sensors, 19.","DOI":"10.3390\/s19040980"},{"key":"ref_32","first-page":"148081","article-title":"Multitarget Tracking with Spatial Nonmaximum Suppressed Sensor Selection","volume":"2015","author":"Ma","year":"2015","journal-title":"Math. Probl. Eng."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"903682","DOI":"10.1155\/2015\/903682","article-title":"Distributed Multiagent Control Approach for Multitarget Tracking","volume":"2015","author":"Ma","year":"2015","journal-title":"Math. Probl. Eng."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"260","DOI":"10.1016\/j.sigpro.2017.07.031","article-title":"Multi-sensor Control for Multi-object Bayes Filters","volume":"142","author":"Wang","year":"2018","journal-title":"Signal Process."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"5191","DOI":"10.1109\/TSP.2016.2595500","article-title":"Sensor Selection for Target Tracking in Wireless Sensor Networks with Uncertainty","volume":"64","author":"Cao","year":"2016","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_36","unstructured":"Fantacci, C., Vo, B.N., Vo, B.T., Battistelli, G., and Chisci, L. (2015). Consensus Labeled Random Finite Set Filtering for Distributed Multi-Object Tracking. arXiv."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Grundel, D., Murphey, R., and Pardalos, P.M. (2004). Multitarget Sensor Management of Dispersed Mobile Sensors. Theory and Algorithms for Cooperative Systems, World Scientific.","DOI":"10.1142\/5635"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"4187","DOI":"10.1109\/TCYB.2019.2935762","article-title":"Pareto Self-Paced Learning Based on Differential Evolution","volume":"51","author":"Li","year":"2021","journal-title":"IEEE Trans. Cybern."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"234","DOI":"10.1109\/TEVC.2016.2598858","article-title":"A Multiobjective Cooperative Coevolutionary Algorithm for Hyperspectral Sparse Unmixing","volume":"21","author":"Gong","year":"2017","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"288","DOI":"10.1109\/TEVC.2018.2850769","article-title":"Decomposition-Based Evolutionary Multiobjective Optimization to Self-Paced Learning","volume":"23","author":"Gong","year":"2019","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"144","DOI":"10.1016\/j.ins.2016.10.035","article-title":"A Decomposition-based Multiobjective Evolutionary Algorithm for Analyzing Network Structural Balance","volume":"378","author":"Ma","year":"2017","journal-title":"Inf. Sci."},{"key":"ref_42","unstructured":"Ngatchou, P., Zarei, A., and El-Sharkawi, A. (2005, January 6\u201310). Pareto Multi-Objective Optimization. Proceedings of the 2005 13th International Conference on, Intelligent Systems Application to Power Systems, Arlington, VA, USA."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"288","DOI":"10.1016\/S0167-6911(82)80025-X","article-title":"Control Problems of Grey Systems","volume":"1","author":"Deng","year":"1982","journal-title":"Syst. Control Lett."},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Ristic, B., Arulampalam, S., and Gordon, N. (2004). Beyond the Kalman Filter-Particle Filters for Tracking Applications, Artech House.","DOI":"10.1155\/S1110865704405095"},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Willis, N.J., and Griffiths, H.D. (2007). Advances in Bistatic Radar, SciTech Publishing Inc.","DOI":"10.1049\/SBRA001E"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"508","DOI":"10.1049\/iet-rsn.2011.0395","article-title":"Target Tracking via Multi-static Doppler Shifts","volume":"7","author":"Ristic","year":"2013","journal-title":"IET Radar Sonar Navig."},{"key":"ref_47","unstructured":"Mahafza, B. (2013). Radar Systems Analysis and Design Using MATLAB, Chapman and Hall\/CRC Press. [3rd ed.]."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"3447","DOI":"10.1109\/TSP.2008.920469","article-title":"A Consistent Metric for Performance Evaluation of Multi-Object Filters","volume":"56","author":"Schuhmacher","year":"2008","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"2754","DOI":"10.1109\/TSP.2020.2986136","article-title":"A Solution for Large-Scale Multi-Object Tracking","volume":"68","author":"Beard","year":"2020","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_50","doi-asserted-by":"crossref","unstructured":"Beard, M., Vo, B.T., and Vo, B.N. (2018, January 10\u201313). Performance Evaluation for Large-Scale Multi-Target Tracking Algorithms. Proceedings of the 2018 21st International Conference on Information Fusion (FUSION), Cambridge, UK.","DOI":"10.23919\/ICIF.2018.8455700"}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/15\/3624\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:58:43Z","timestamp":1760140723000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/15\/3624"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,7,28]]},"references-count":50,"journal-issue":{"issue":"15","published-online":{"date-parts":[[2022,8]]}},"alternative-id":["rs14153624"],"URL":"https:\/\/doi.org\/10.3390\/rs14153624","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,7,28]]}}}