Multi-target elliptic positioning via difference of convex functions programming
Multi-target localization in a distributed multiple-input multiple-output radar is quite challenging as the correct measurement-target associations in each transmitter–receiver pair are unknown. In this paper, we address this difficult problem from a joint optimization perspective. The measurement-t...
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| Published in: | Signal processing Vol. 234; p. 109996 |
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01.09.2025
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| Abstract | Multi-target localization in a distributed multiple-input multiple-output radar is quite challenging as the correct measurement-target associations in each transmitter–receiver pair are unknown. In this paper, we address this difficult problem from a joint optimization perspective. The measurement-target association and multi-target localization are jointly formulated as an intractable mixed-integer optimization problem, which contains both discrete and continuous variables. We first develop an equivalent Difference of Convex functions (DC) representation for the non-convex Boolean constraint imposed on the association variables, making the problem tractable. Then, a DC algorithm is derived to efficiently solve the resulting optimization problem. Simulation results demonstrate that the proposed DC method is numerically accurate when compared to state-of-the-art methods. |
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| AbstractList | Multi-target localization in a distributed multiple-input multiple-output radar is quite challenging as the correct measurement-target associations in each transmitter–receiver pair are unknown. In this paper, we address this difficult problem from a joint optimization perspective. The measurement-target association and multi-target localization are jointly formulated as an intractable mixed-integer optimization problem, which contains both discrete and continuous variables. We first develop an equivalent Difference of Convex functions (DC) representation for the non-convex Boolean constraint imposed on the association variables, making the problem tractable. Then, a DC algorithm is derived to efficiently solve the resulting optimization problem. Simulation results demonstrate that the proposed DC method is numerically accurate when compared to state-of-the-art methods. |
| ArticleNumber | 109996 |
| Author | Yan, Junkun Liu, Hongwei Dang, Xudong |
| Author_xml | – sequence: 1 givenname: Xudong surname: Dang fullname: Dang, Xudong email: dangxudong@xidian.edu.cn – sequence: 2 givenname: Hongwei surname: Liu fullname: Liu, Hongwei email: hwliu@xidian.edu.cn – sequence: 3 givenname: Junkun orcidid: 0000-0002-3828-6812 surname: Yan fullname: Yan, Junkun email: jkyan@xidian.edu.cn |
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| Keywords | Difference of convex functions Multi-target localization Convex optimization Distributed MIMO radar Data association |
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| References | He, Blum, Haimovich (b2) 2010; 58 Godrich, Haimovich, Blum (b1) 2010; 56 Shen, Ding, Dasgupta, Zhao (b17) 2014; 62 Amiri, Behnia, Zamani (b10) 2017; 24 Liang, Wang, Su, Chen, Chen, So (b11) 2016; 122 Shi, Wang, Leung, So, EURASIP (b12) 2020; 174 Yu, Li, Guo, Sun (b13) 2020; 27 Dianat, Taban, Dianat, Sedighi (b4) 2013; 49 Deb, Yeddanapudi, Pattipati, Bar-Shalom (b16) 1997; 33 Horst, Thoai (b20) 1999; 103 Panwar, Babu (b14) 2022; 29 Le Thi, Pham Dinh (b21) 2018; 169 Wu, Ding, Sun, Toh (b22) 2014; 24 Noroozi, Sebt, Hosseini, Amiri, Nayebi (b7) 2020; 56 Zhang, Liu, Zhang, Liu (b3) 2024 Grant, Boyd (b23) 2014 Kazemi, Amiri, Behnia (b18) 2021; 25 Dang, Liu, Yan (b15) 2024; 31 Amiri, Behnia (b5) 2017; 24 Panwar, Babu, Stoica (b8) 2022; 29 J.-y. Gotoh, Takeda, Tono (b19) 2018; 169 Lobo, Vandenberghe, Boyd, Lebret (b24) 1998; 284 Park, Chang (b6) 2015; 15 Liang, Leung, So (b9) 2015; 64 Dianat (10.1016/j.sigpro.2025.109996_b4) 2013; 49 Grant (10.1016/j.sigpro.2025.109996_b23) 2014 J.-y. Gotoh (10.1016/j.sigpro.2025.109996_b19) 2018; 169 Zhang (10.1016/j.sigpro.2025.109996_b3) 2024 Godrich (10.1016/j.sigpro.2025.109996_b1) 2010; 56 Horst (10.1016/j.sigpro.2025.109996_b20) 1999; 103 Shi (10.1016/j.sigpro.2025.109996_b12) 2020; 174 Deb (10.1016/j.sigpro.2025.109996_b16) 1997; 33 Wu (10.1016/j.sigpro.2025.109996_b22) 2014; 24 Lobo (10.1016/j.sigpro.2025.109996_b24) 1998; 284 Noroozi (10.1016/j.sigpro.2025.109996_b7) 2020; 56 Yu (10.1016/j.sigpro.2025.109996_b13) 2020; 27 Shen (10.1016/j.sigpro.2025.109996_b17) 2014; 62 Liang (10.1016/j.sigpro.2025.109996_b9) 2015; 64 Amiri (10.1016/j.sigpro.2025.109996_b10) 2017; 24 He (10.1016/j.sigpro.2025.109996_b2) 2010; 58 Amiri (10.1016/j.sigpro.2025.109996_b5) 2017; 24 Park (10.1016/j.sigpro.2025.109996_b6) 2015; 15 Dang (10.1016/j.sigpro.2025.109996_b15) 2024; 31 Kazemi (10.1016/j.sigpro.2025.109996_b18) 2021; 25 Liang (10.1016/j.sigpro.2025.109996_b11) 2016; 122 Panwar (10.1016/j.sigpro.2025.109996_b14) 2022; 29 Le Thi (10.1016/j.sigpro.2025.109996_b21) 2018; 169 Panwar (10.1016/j.sigpro.2025.109996_b8) 2022; 29 |
| References_xml | – volume: 62 start-page: 1938 year: 2014 end-page: 1949 ident: b17 article-title: Multiple source localization in wireless sensor networks based on time of arrival measurement publication-title: IEEE Trans. Signal Process. – volume: 58 start-page: 3661 year: 2010 end-page: 3680 ident: b2 article-title: Noncoherent MIMO radar for location and velocity estimation: More antennas means better performance publication-title: IEEE Trans. Signal Process. – volume: 56 start-page: 3123 year: 2020 end-page: 3133 ident: b7 article-title: Closed-form solution for elliptic localization in distributed MIMO radar systems with minimum number of sensors publication-title: IEEE Trans. Aerosp. Electron. Syst. – volume: 24 start-page: 766 year: 2014 end-page: 794 ident: b22 article-title: On the moreau–yosida regularization of the vector k-norm related functions publication-title: SIAM J. Optim. – volume: 64 start-page: 1574 year: 2015 end-page: 1585 ident: b9 article-title: Lagrange programming neural network approach for target localization in distributed MIMO radar publication-title: IEEE Trans. Signal Process. – volume: 24 start-page: 902 year: 2017 end-page: 906 ident: b5 article-title: An efficient weighted least squares estimator for elliptic localization in distributed MIMO radars publication-title: IEEE Signal Process. Lett. – volume: 15 start-page: 1480 year: 2015 end-page: 1490 ident: b6 article-title: Closed-form localization for distributed MIMO radar systems using time delay measurements publication-title: IEEE Trans. Wirel. Commun. – volume: 103 start-page: 1 year: 1999 end-page: 43 ident: b20 article-title: DC programming: overview publication-title: J. Optim. Theory Appl. – volume: 24 start-page: 299 year: 2017 end-page: 303 ident: b10 article-title: Asymptotically efficient target localization from bistatic range measurements in distributed MIMO radars publication-title: IEEE Signal Process. Lett. – volume: 25 start-page: 2904 year: 2021 end-page: 2907 ident: b18 article-title: Data association for multi-target elliptic localization in distributed MIMO radars publication-title: IEEE Commun. Lett. – volume: 169 start-page: 5 year: 2018 end-page: 68 ident: b21 article-title: DC programming and DCA: thirty years of developments publication-title: Math. Program. – volume: 29 start-page: 847 year: 2022 end-page: 851 ident: b8 article-title: Maximum likelihood algorithm for time-delay based multistatic target localization publication-title: IEEE Signal Process. Lett. – volume: 122 start-page: 33 year: 2016 end-page: 38 ident: b11 article-title: Robust MIMO radar target localization via nonconvex optimization publication-title: Signal Process. – year: 2014 ident: b23 article-title: CVX: Matlab software for disciplined convex programming, version 2.1 – volume: 33 start-page: 523 year: 1997 end-page: 538 ident: b16 article-title: A generalized SD assignment algorithm for multisensor-multitarget state estimation publication-title: IEEE Trans. Aerosp. Electron. Syst. – volume: 27 start-page: 2168 year: 2020 end-page: 2172 ident: b13 article-title: Message passing based robust target localization in distributed MIMO radars in the presence of outliers publication-title: IEEE Signal Process. Lett. – volume: 29 start-page: 2632 year: 2022 end-page: 2636 ident: b14 article-title: Robust multistatic target localization in the presence of NLOS errors and outliers publication-title: IEEE Signal Process. Lett. – volume: 56 start-page: 2783 year: 2010 end-page: 2803 ident: b1 article-title: Target localization accuracy gain in MIMO radar-based systems publication-title: IEEE Trans. Inform. Theory – volume: 31 start-page: 2110 year: 2024 end-page: 2114 ident: b15 article-title: Robust elliptic positioning via sparse regularization and ADMM for a distributed MIMO radar in the presence of outliers publication-title: IEEE Signal Process. Lett. – volume: 284 start-page: 193 year: 1998 end-page: 228 ident: b24 article-title: Applications of second-order cone programming publication-title: Linear Algebra Appl. – volume: 174 year: 2020 ident: b12 article-title: Robust MIMO radar target localization based on lagrange programming neural network publication-title: Signal Process. – volume: 169 start-page: 141 year: 2018 end-page: 176 ident: b19 article-title: DC formulations and algorithms for sparse optimization problems publication-title: Math. Program. – year: 2024 ident: b3 article-title: Joint customer assignment, power allocation, and subchannel allocation in a uav-based joint radar and communication network publication-title: IEEE Internet Things J. – volume: 49 start-page: 2730 year: 2013 end-page: 2741 ident: b4 article-title: Target localization using least squares estimation for MIMO radars with widely separated antennas publication-title: IEEE Trans. Aerosp. Electron. Syst. – volume: 33 start-page: 523 issue: 2 year: 1997 ident: 10.1016/j.sigpro.2025.109996_b16 article-title: A generalized SD assignment algorithm for multisensor-multitarget state estimation publication-title: IEEE Trans. Aerosp. Electron. Syst. doi: 10.1109/7.575891 – volume: 169 start-page: 141 year: 2018 ident: 10.1016/j.sigpro.2025.109996_b19 article-title: DC formulations and algorithms for sparse optimization problems publication-title: Math. Program. doi: 10.1007/s10107-017-1181-0 – volume: 15 start-page: 1480 issue: 2 year: 2015 ident: 10.1016/j.sigpro.2025.109996_b6 article-title: Closed-form localization for distributed MIMO radar systems using time delay measurements publication-title: IEEE Trans. Wirel. Commun. doi: 10.1109/TWC.2015.2490677 – volume: 24 start-page: 299 issue: 3 year: 2017 ident: 10.1016/j.sigpro.2025.109996_b10 article-title: Asymptotically efficient target localization from bistatic range measurements in distributed MIMO radars publication-title: IEEE Signal Process. Lett. doi: 10.1109/LSP.2017.2660545 – volume: 56 start-page: 2783 issue: 6 year: 2010 ident: 10.1016/j.sigpro.2025.109996_b1 article-title: Target localization accuracy gain in MIMO radar-based systems publication-title: IEEE Trans. Inform. Theory doi: 10.1109/TIT.2010.2046246 – volume: 62 start-page: 1938 issue: 8 year: 2014 ident: 10.1016/j.sigpro.2025.109996_b17 article-title: Multiple source localization in wireless sensor networks based on time of arrival measurement publication-title: IEEE Trans. Signal Process. doi: 10.1109/TSP.2014.2304433 – year: 2024 ident: 10.1016/j.sigpro.2025.109996_b3 article-title: Joint customer assignment, power allocation, and subchannel allocation in a uav-based joint radar and communication network publication-title: IEEE Internet Things J. – volume: 58 start-page: 3661 issue: 7 year: 2010 ident: 10.1016/j.sigpro.2025.109996_b2 article-title: Noncoherent MIMO radar for location and velocity estimation: More antennas means better performance publication-title: IEEE Trans. Signal Process. doi: 10.1109/TSP.2010.2044613 – volume: 25 start-page: 2904 issue: 9 year: 2021 ident: 10.1016/j.sigpro.2025.109996_b18 article-title: Data association for multi-target elliptic localization in distributed MIMO radars publication-title: IEEE Commun. Lett. doi: 10.1109/LCOMM.2021.3087009 – volume: 284 start-page: 193 issue: 1–3 year: 1998 ident: 10.1016/j.sigpro.2025.109996_b24 article-title: Applications of second-order cone programming publication-title: Linear Algebra Appl. doi: 10.1016/S0024-3795(98)10032-0 – volume: 122 start-page: 33 year: 2016 ident: 10.1016/j.sigpro.2025.109996_b11 article-title: Robust MIMO radar target localization via nonconvex optimization publication-title: Signal Process. doi: 10.1016/j.sigpro.2015.11.004 – volume: 29 start-page: 2632 year: 2022 ident: 10.1016/j.sigpro.2025.109996_b14 article-title: Robust multistatic target localization in the presence of NLOS errors and outliers publication-title: IEEE Signal Process. Lett. doi: 10.1109/LSP.2022.3231494 – volume: 169 start-page: 5 issue: 1 year: 2018 ident: 10.1016/j.sigpro.2025.109996_b21 article-title: DC programming and DCA: thirty years of developments publication-title: Math. Program. doi: 10.1007/s10107-018-1235-y – volume: 174 year: 2020 ident: 10.1016/j.sigpro.2025.109996_b12 article-title: Robust MIMO radar target localization based on lagrange programming neural network publication-title: Signal Process. doi: 10.1016/j.sigpro.2020.107574 – volume: 64 start-page: 1574 issue: 6 year: 2015 ident: 10.1016/j.sigpro.2025.109996_b9 article-title: Lagrange programming neural network approach for target localization in distributed MIMO radar publication-title: IEEE Trans. Signal Process. doi: 10.1109/TSP.2015.2500881 – volume: 103 start-page: 1 year: 1999 ident: 10.1016/j.sigpro.2025.109996_b20 article-title: DC programming: overview publication-title: J. Optim. Theory Appl. doi: 10.1023/A:1021765131316 – volume: 56 start-page: 3123 issue: 4 year: 2020 ident: 10.1016/j.sigpro.2025.109996_b7 article-title: Closed-form solution for elliptic localization in distributed MIMO radar systems with minimum number of sensors publication-title: IEEE Trans. Aerosp. Electron. Syst. doi: 10.1109/TAES.2020.2965668 – volume: 31 start-page: 2110 year: 2024 ident: 10.1016/j.sigpro.2025.109996_b15 article-title: Robust elliptic positioning via sparse regularization and ADMM for a distributed MIMO radar in the presence of outliers publication-title: IEEE Signal Process. Lett. doi: 10.1109/LSP.2024.3443454 – year: 2014 ident: 10.1016/j.sigpro.2025.109996_b23 – volume: 49 start-page: 2730 issue: 4 year: 2013 ident: 10.1016/j.sigpro.2025.109996_b4 article-title: Target localization using least squares estimation for MIMO radars with widely separated antennas publication-title: IEEE Trans. Aerosp. Electron. Syst. doi: 10.1109/TAES.2013.6621849 – volume: 29 start-page: 847 year: 2022 ident: 10.1016/j.sigpro.2025.109996_b8 article-title: Maximum likelihood algorithm for time-delay based multistatic target localization publication-title: IEEE Signal Process. Lett. doi: 10.1109/LSP.2022.3158592 – volume: 27 start-page: 2168 year: 2020 ident: 10.1016/j.sigpro.2025.109996_b13 article-title: Message passing based robust target localization in distributed MIMO radars in the presence of outliers publication-title: IEEE Signal Process. Lett. doi: 10.1109/LSP.2020.3042456 – volume: 24 start-page: 902 issue: 6 year: 2017 ident: 10.1016/j.sigpro.2025.109996_b5 article-title: An efficient weighted least squares estimator for elliptic localization in distributed MIMO radars publication-title: IEEE Signal Process. Lett. doi: 10.1109/LSP.2017.2697500 – volume: 24 start-page: 766 issue: 2 year: 2014 ident: 10.1016/j.sigpro.2025.109996_b22 article-title: On the moreau–yosida regularization of the vector k-norm related functions publication-title: SIAM J. Optim. doi: 10.1137/110827144 |
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| Title | Multi-target elliptic positioning via difference of convex functions programming |
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