{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,17]],"date-time":"2025-10-17T14:26:48Z","timestamp":1760711208093,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"13","license":[{"start":{"date-parts":[[2023,7,3]],"date-time":"2023-07-03T00:00:00Z","timestamp":1688342400000},"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":["62271247","JCKY2021210B004"],"award-info":[{"award-number":["62271247","JCKY2021210B004"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Defense Industrial Technology Development Program","award":["62271247","JCKY2021210B004"],"award-info":[{"award-number":["62271247","JCKY2021210B004"]}]},{"name":"Prospective Layout of Scientific Research for NUAA (Nanjing University of Aeronautics and Astronautics)","award":["62271247","JCKY2021210B004"],"award-info":[{"award-number":["62271247","JCKY2021210B004"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>This paper develops a collaborative trajectory planning and resource allocation (CTPRA) strategy for multi-target tracking (MTT) in a spectral coexistence environment utilizing airborne radar networks. The key mechanism of the proposed strategy is to jointly design the flight trajectory and optimize the radar assignment, transmit power, dwell time, and signal effective bandwidth allocation of multiple airborne radars, aiming to enhance the MTT performance under the constraints of the tolerable threshold of interference energy, platform kinematic limitations, and given illumination resource budgets. The closed-form expression for the Bayesian Cram\u00e9r\u2013Rao lower bound (BCRLB) under the consideration of spectral coexistence is calculated and adopted as the optimization criterion of the CTPRA strategy. It is shown that the formulated CTPRA problem is a mixed-integer programming, non-linear, non-convex optimization model owing to its highly coupled Boolean and continuous parameters. By incorporating semi-definite programming (SDP), particle swarm optimization (PSO), and the cyclic minimization technique, an iterative four-stage solution methodology is proposed to tackle the formulated optimization problem efficiently. The numerical results validate the effectiveness and the MTT performance improvement of the proposed CTPRA strategy in comparison with other benchmarks.<\/jats:p>","DOI":"10.3390\/rs15133386","type":"journal-article","created":{"date-parts":[[2023,7,4]],"date-time":"2023-07-04T01:38:32Z","timestamp":1688434712000},"page":"3386","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Collaborative Trajectory Planning and Resource Allocation for Multi-Target Tracking in Airborne Radar Networks under Spectral Coexistence"],"prefix":"10.3390","volume":"15","author":[{"given":"Chenguang","family":"Shi","sequence":"first","affiliation":[{"name":"Key Laboratory of Radar Imaging and Microwave Photonics (Nanjing University of Aeronautics and Astronautics), Ministry of Education, Nanjing 210016, China"}]},{"given":"Jing","family":"Dong","sequence":"additional","affiliation":[{"name":"Key Laboratory of Radar Imaging and Microwave Photonics (Nanjing University of Aeronautics and Astronautics), Ministry of Education, Nanjing 210016, China"},{"name":"No. 8511 Research Institute of CASIC, Nanjing 210007, China"}]},{"given":"Sana","family":"Salous","sequence":"additional","affiliation":[{"name":"Department of Engineering, Durham University, Durham DH1 3DE, UK"}]},{"given":"Ziwei","family":"Wang","sequence":"additional","affiliation":[{"name":"Beijing Institute of Control and Electronics Technology, Beijing 100045, China"}]},{"given":"Jianjiang","family":"Zhou","sequence":"additional","affiliation":[{"name":"Key Laboratory of Radar Imaging and Microwave Photonics (Nanjing University of Aeronautics and Astronautics), Ministry of Education, Nanjing 210016, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,7,3]]},"reference":[{"key":"ref_1","first-page":"1551","article-title":"Joint aperture and transmit resource allocation strategy for multitarget localization in the phased array radar network","volume":"59","author":"Zhang","year":"2023","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"7705","DOI":"10.1109\/JSEN.2023.3249782","article-title":"Joint power allocation and route planning scheme for multitarget tracking in airborne radar network under multiuncertainty","volume":"23","author":"Zhang","year":"2023","journal-title":"IEEE Sens. J."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"729","DOI":"10.1109\/TSP.2017.2777394","article-title":"Joint node selection and power allocation strategy for multitarget tracking in decentralized radar networks","volume":"66","author":"Xie","year":"2018","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"5833","DOI":"10.1109\/TSP.2022.3188205","article-title":"Joint detection threshold optimization and illumination time allocation strategy for cognitive tracking in a networked radar system","volume":"70","author":"Zhang","year":"2022","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1602","DOI":"10.1109\/TSP.2020.2976587","article-title":"Resource scheduling for distributed multi-target tracking in netted colocated MIMO radar systems","volume":"68","author":"Yi","year":"2020","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1863","DOI":"10.1109\/LSP.2021.3108675","article-title":"Joint radar scheduling and beampattern design for multitarget tracking in netted colocated MIMO radar systems","volume":"28","author":"Sun","year":"2021","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_7","first-page":"1","article-title":"Composed resource optimization for multitarget tracking in active and passive radar network","volume":"60","author":"Dai","year":"2022","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"3196","DOI":"10.1109\/JSEN.2019.2954711","article-title":"Time and aperture resource allocation strategy for multitarget ISAR imaging in a radar network","volume":"20","author":"Du","year":"2020","journal-title":"IEEE Sens. J."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"19570","DOI":"10.1109\/JSEN.2021.3090053","article-title":"Joint optimization of time and aperture resource allocation strategy for multi-target ISAR imaging in radar sensor network","volume":"21","author":"Wang","year":"2021","journal-title":"IEEE Sens. J."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Su, Y., Cheng, T., and He, Z.S. (2023). Joint resource and detection threshold optimization for maneuvering targets tracking in colocated MIMO radar network. IEEE Trans. Aerosp. Electron. Syst.","DOI":"10.1109\/TAES.2023.3267336"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1016\/j.inffus.2019.08.010","article-title":"Collaborative detection and power allocation framework for target tracking in multiple radar system","volume":"55","author":"Yan","year":"2020","journal-title":"Inf. Fusion"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"107650","DOI":"10.1016\/j.sigpro.2020.107650","article-title":"Joint time-space resource allocation and waveform selection for the collocated MIMO radar in multiple targets tracking","volume":"176","author":"Li","year":"2020","journal-title":"Signal Process."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2858","DOI":"10.1109\/TAP.2010.2052573","article-title":"Low probability of intercept antenna array beamforming","volume":"58","author":"Lawrence","year":"2010","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1351","DOI":"10.1109\/TAES.2013.6494419","article-title":"Low probability of intercept of an advanced noise radar waveform with linear-FM","volume":"49","author":"Govoni","year":"2013","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1316","DOI":"10.1109\/TSP.2017.2770086","article-title":"Power minimization-based robust OFDM radar waveform design for radar and communication systems in coexistence","volume":"66","author":"Shi","year":"2018","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1099","DOI":"10.1109\/TVT.2017.2704610","article-title":"A robust and efficient algorithm for coprime array adaptive beamforming","volume":"67","author":"Zhou","year":"2018","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"6669","DOI":"10.1109\/JSYST.2021.3134657","article-title":"Joint route optimization and multidimensional resource management scheme for airborne radar network in target tracking application","volume":"16","author":"Shi","year":"2022","journal-title":"IEEE Syst. J."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1109\/TSP.2020.3047519","article-title":"Robust power allocation for resource-aware multi-target tracking with colocated MIMO radars","volume":"69","author":"Yuan","year":"2021","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2762","DOI":"10.1109\/TAES.2021.3138869","article-title":"Joint transmit resource management and waveform selection strategy for target tracking in distributed phased array radar network","volume":"58","author":"Shi","year":"2022","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"3960","DOI":"10.1109\/JSYST.2021.3098622","article-title":"Joint waveform control and resource optimization for maneuvering targets tracking in netted colocated MIMO radar systems","volume":"16","author":"Su","year":"2022","journal-title":"IEEE Syst. J."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1264","DOI":"10.1109\/JSYST.2020.2984774","article-title":"Data-driven simultaneous multibeam power allocation: When multiple targets tracking meets deep reinforcement learning","volume":"15","author":"Shi","year":"2021","journal-title":"IEEE Syst. J."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"6397","DOI":"10.1109\/TSP.2017.2755591","article-title":"Game-theoretic power allocation and the Nash equilibrium analysis for a multistatic MIMO radar network","volume":"65","author":"Deligiannis","year":"2017","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"3946","DOI":"10.1109\/TSP.2018.2841865","article-title":"Robust chance constrained power allocation scheme for multiple target localization in colocated MIMO radar system","volume":"66","author":"Yan","year":"2018","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"4379","DOI":"10.1109\/JSYST.2020.3025867","article-title":"Joint target assignment and resource optimization framework for multitarget tracking in phased array radar network","volume":"15","author":"Shi","year":"2021","journal-title":"IEEE Syst. J."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"3504","DOI":"10.1109\/TSP.2018.2831624","article-title":"Joint system design for coexistence of MIMO radar and communication","volume":"66","author":"Qian","year":"2018","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"5891","DOI":"10.1109\/TSP.2021.3121090","article-title":"Radar and communication spectral coexistence in range-dependent interference","volume":"69","author":"Qian","year":"2021","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2314","DOI":"10.1109\/TAES.2018.2884806","article-title":"Radar waveform optimization for target parameter estimation in cooperative radar-communications systems","volume":"55","author":"Bica","year":"2019","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1603","DOI":"10.1109\/TSP.2021.3060003","article-title":"Power allocation for coexisting multicarrier radar and communication systems in cluttered environment","volume":"69","author":"Wang","year":"2021","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1049\/iet-rsn.2019.0215","article-title":"Communication-awareness joint beams and power allocation scheme of radar network for manoeuvring targets tracking","volume":"14","author":"Lu","year":"2020","journal-title":"IET Radar Sonar Navig."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"750","DOI":"10.1049\/sil2.12097","article-title":"Communication-awareness adaptive resource scheduling strategy for multiple target tracking in a multiple radar system","volume":"16","author":"Su","year":"2022","journal-title":"IET Signal Process."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"2026","DOI":"10.1109\/JSAC.2022.3157371","article-title":"Resource allocation in heterogeneously-distributed joint radar-communication under asynchronous Bayesian tracking framework","volume":"40","author":"Wu","year":"2022","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Boyd, S.P., and Vandenberghe, L. (2004). Convex Optimization, Cambridge University Press.","DOI":"10.1017\/CBO9780511804441"}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/13\/3386\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T20:05:12Z","timestamp":1760126712000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/13\/3386"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,7,3]]},"references-count":32,"journal-issue":{"issue":"13","published-online":{"date-parts":[[2023,7]]}},"alternative-id":["rs15133386"],"URL":"https:\/\/doi.org\/10.3390\/rs15133386","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2023,7,3]]}}}