A Hybrid Approach to Optimal TOA-Sensor Placement With Fixed Shared Sensors for Simultaneous Multi-Target Localization

[en] This paper focuses on optimal time-of-arrival (TOA) sensor placement for multiple target localization simultaneously. In previous work, different solutions only using non-shared sensors to localize multiple targets have been developed. Those methods localize different targets one-by-one or use a large number of mobile sensors with many limitations, such as low effectiveness and high network complexity. In this paper, firstly, a novel optimization model for multi-target localization incorporating shared sensors is formulated. Secondly, the systematic theoretical results of the optimal sensor placement are derived and concluded using the A-optimality criterion, i.e., minimizing the trace of the inverse Fisher information matrix (FIM), based on rigorous geometrical derivations. The reachable optimal trace of Cramér-Rao lower bound (CRLB) is also derived. It can provide optimal conditions for many cases and even closed form solutions for some special cases. Thirdly, a novel numerical optimization algorithm to quickly find and calculate the (sub-)optimal placement and achievable lower bound is explored, when the model becomes complicated with more practical constraints. Then, a hybrid method for solving the most general situation, integrating both the analytical and numerical solutions, is proposed. Finally, the correctness and effectiveness of the proposed theoretical and mathematical methods are demonstrated by several simulation examples.

Disciplines :

Electrical & electronics engineering

Author, co-author :

Xu, Sheng; Shenzhen Institute of Advanced Technology

Wu, Linlong ; University of Luxembourg > Interdisciplinary Centre for Security, Reliability and Trust (SNT) > SPARC

Doğançay, Kutluyıl; University of South Australia > UniSA STEM

Other collaborator :

Alaeekerahroodi, Mohammad ; University of Luxembourg > Interdisciplinary Centre for Security, Reliability and Trust (SNT) > SPARC

External co-authors :

yes

Language :

English

Title :

A Hybrid Approach to Optimal TOA-Sensor Placement With Fixed Shared Sensors for Simultaneous Multi-Target Localization

Publication date :

23 February 2022

Journal title :

IEEE Transactions on Signal Processing

ISSN :

1053-587X

Publisher :

Institute of Electrical and Electronics Engineers, United States

Peer reviewed :

Peer Reviewed verified by ORBi

European Projects :

H2020 - 742648 - AGNOSTIC - Actively Enhanced Cognition based Framework for Design of Complex Systems

FnR Project :

FNR12734677 - Signal Processing For Next Generation Radar, 2018 (01/09/2019-31/08/2022) - Bjorn Ottersten

Funders :

CE - Commission Européenne [BE]

Available on ORBilu :

since 11 January 2023

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Bibliography

M. Z. Win, Y. Shen, and W. Dai, "A theoretical foundation of network localization and navigation," Proc. IEEE, vol. 106, no. 7, pp. 1136-1165, Jul. 2018.
M. Chiani, A. Giorgetti, and E. Paolini, "Sensor radar for object tracking," Proc. IEEE, vol. 106, no. 6, pp. 1022-1041, Jun. 2018.
A. Conti, S. Mazuelas, S. Bartoletti, W. C. Lindsey, and M. Z. Win, "Soft information for localization-of-things," Proc. IEEE, vol. 107, no. 11, pp. 2240-2264, Nov. 2019.
S. Xu, J. Liu, C. Yang, X. Wu, and T. Xu, "A learning-based stable servo control strategy using broad learning system applied formicrorobotic control," IEEE Trans. Cybern., pp. 1-11, doi: 10.1109/TCYB.2021.3121080.
A. N. Bishop, B. Fidan, B. Anderson, K. Dogançay, and P. N. Pathirana, "Optimality analysis of sensor-target localization geometries," Automatica, vol. 46, no. 3, pp. 479-492, 2010.
N. H. Nguyen and K. Dogançay, "Optimal geometry analysis for multistatic TOA localization," IEEE Trans. Signal Process., vol. 64, no. 16, pp. 4180-4193, Aug. 2016.
X. R. Li, "RSS-based location estimation with unknown pathloss model," IEEE Trans. Wireless Commun., vol. 5, no. 12, pp. 3626-3633, Dec. 2006.
H. C. So, "Source localization: Algorithms and analysis," in Handbook Position Location: Theory, Pract., Advances, 2011.
S. Chen and K. C. Ho, "Achieving asymptotic efficient performance for squared range and squared range difference localizations," IEEE Trans. Signal Process., vol. 61, no. 11, pp. 2836-2849, Jun. 2013.
A. Beck, P. Stoica, and J. Li, "Exact and approximate solutions of source localization problems," IEEE Trans. Signal Process., vol. 56, no. 5, pp. 1770-1778, May 2008.
V. J. Aidala, "Kalman filter behavior in bearings-only tracking applications," IEEE Trans. Aerosp. Electron. Syst., vol.AES-15, no. 1, pp. 29-39, Jan. 1979.
S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory. Englewood Cliffs, NJ, USA: Prentice-Hall, 1993.
K. Dogançay, "Bias compensation for the bearings-only pseudolinear target track estimator," IEEE Trans. Signal Process., vol. 54, no. 1, pp. 59-68, Jan. 2006.
S. Xu, K. Dogançay, and H. Hmam, "Distributed pseudolinear estimation and UAV path optimization for 3D AOA target tracking," Signal Process., vol. 133, pp. 64-78, 2017.
S. C. Nardone, A. G. Lindgren, and K. F. Gong, "Fundamental properties and performance of conventional bearings-only target motion analysis," IEEE Trans. Autom. Control, vol. AC-29, no. 9, pp. 775-787, Sep. 1984.
M. S. Arulampalam, S. Maskell, N. Gordon, and T. Clapp, "A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking," IEEE Trans. Signal Process., vol. 50, no. 2, pp. 174-188, Feb. 2002.
J. A. Fawcett, "Effect of course maneuvers on bearings-only range estimation," IEEE Trans. Acoust., Speech Signal Process., vol. 36, no. 8, pp. 1193-1199, Aug. 1988.
Y. Oshman and P. Davidson, "Optimization of observer trajectories for bearings-only target localization," IEEE Trans. Aerosp. Electron. Syst., vol. 35, no. 3, pp. 892-902, Jul. 1999.
S. Xu, Y. Ou, and X. Wu, "Optimal sensor placement for 3-D time-ofarrival target localization," IEEE Trans. Signal Process., vol. 67, no. 19, pp. 5018-5031, Oct. 2019.
D. Moreno-Salinas, A. Pascoal, and J. Aranda, "Optimal sensor placement for acoustic underwater target positioning with range-onlymeasurements," IEEE J. Ocean. Eng., vol. 41, no. 3, pp. 620-643, Jul. 2016.
D. Ucinski, Optimal Measurement Methods for Distributed Parameter System Identification. Boca Raton, FL, USA: CRC Press, 2005.
S. Zhao, B. Chen, and T. H. Lee, "Optimal sensor placement for target localization and tracking in 2D and 3D," Int. J. Control, vol. 86, no. 10, pp. 1687-1704, 2013.
L. Rui and K. C. Ho, "Elliptic localization: Performance study and optimum receiver placement," IEEE Trans. Signal Process., vol. 62, no. 18, pp. 4673-4688, Sep. 2014.
S. Xu and K. Dogançay, "Optimal sensor placement for 3-D angle-ofarrival target localization," IEEE Trans. Aerosp. Electron. Syst., vol. 53, no. 3, pp. 1196-1211, Jun. 2017.
D. Moreno-Salinas, A.M. Pascoal, and J. Aranda, "Optimal sensor placement for multiple target positioning with range-only measurements in two-dimensional scenarios," Sensors, vol. 13, no. 8, pp. 10 674-10 710, 2013.
Y. Li, G. Qi, and A. Sheng, "Optimal deployment of vehicles with circular formation for bearings-only multi-target localization," Automatica, vol. 105, pp. 347-355, 2019.
A. M. Aziz, "A novel all-neighbor fuzzy association approach for multitarget tracking in a cluttered environment," Signal Process., vol. 91, no. 8, pp. 2001-2015, 2011.
Y. Bar-Shalom, Multitarget-Multisensor Tracking: Applications and Advances, vol. 3. Norwood, MA, USA: Artech House, 2000.
S. S. Blackman, "Multiple hypothesis tracking for multiple target tracking," IEEE Aerosp. Electron. Syst. Mag., vol. 19, no. 1, pp. 5-18, Jan. 2004.
T. E. Fortmann, Y. Bar-Shalom, and M. Scheffe, "Sonar tracking of multiple targets using joint probabilistic data association," IEEE J. Ocean. Eng., vol. OE-8, no. 3, pp. 173-184, Jul. 1983.
S. Blackrnan and A. House, Design and Analysis of Modern Tracking Systems, Boston, MA, USA: Artech House, 1999.
S. Xu, M. Rice, and F. Rice, "Optimal TOA-sensor placement for two target localization simultaneously using shared sensors," IEEE Commun. Lett., vol. 25, no. 8, pp. 2584-2588, Aug. 2021.
Y. Zhao, R. Schwartz, E. Salomons, A. Ostfeld, and H. V. Poor, "New formulation and optimization methods for water sensor placement," Environmental Modelling Softw., vol. 76, pp. 128-136, 2016.
C. Jiang, Y. Soh, and H. Li, "Sensor placement by maximal projection on minimum eigenspace for linear inverse problems," IEEE Trans. Signal Process., vol. 64, no. 21, pp. 5595-5610, Nov. 2016.
C. Jiang, Z. Chen, R. Su, and Y. Soh, "Group greedy method for sensor placement," IEEE Trans. Signal Process., vol. 67, no. 9, pp. 2249-2262, May 2019.
S. P. Chepuri and G. Leus, "Continuous sensor placement," IEEE Signal Process. Lett., vol. 22, no. 5, pp. 544-548, May 2015.
N. Sahu, L. Wu, P. Babu, B. ShankarM. R., and B. Ottersten, "Optimal sensor placement for source localization: A unified ADMM approach," IEEE Trans. Veh. Technol., pp. 1-1, doi: 10.1109/TVT.2022.3146603.
S. Coraluppi and C. Carthel, "Distributed tracking in multistatic sonar," IEEE Trans. Aerosp. Electron. Syst., vol. 41, no. 3, pp. 1138-1147, Jul. 2005.
A. Munaf, G. Canepa, and K. D. LePage, "Continuous active sonars for littoral undersea surveillance," IEEE J. Ocean. Eng., vol. 44, no. 4, pp. 1198-1212, Oct. 2019.
S. Xu, "Optimal sensor placement for target localization using hybrid RSS, AOA and TOA measurements," IEEE Commun. Lett., vol. 24, no. 9, pp. 1966-1970, Sep. 2020.
D. J. Torrieri, "Statistical theory of passive location systems," IEEE Trans. Aerosp. Electron. Syst., vol. AES-20, no. 2, pp. 183-198, Mar. 1984.
D. Moreno-Salinas, A. Pascoal, and J. Aranda, "Sensor networks for optimal target localization with bearings-only measurements in constrained three-dimensional scenarios," Sensors, vol. 13, no. 8, pp. 10386-10417, 2013.
S. Xu and K. Dogançay, "Optimal sensor deployment for 3D AOA target localization," in Proc. IEEE Int. Conf. Acoust., Speech Signal Process., 2015, pp. 2544-2548.
J. M. Danskin, "The theory of max-min, with applications," SIAM J. Appl. Math., vol. 14, no. 4, pp. 641-664, 1966.
C. Jin, P. Netrapalli, and M. Jordan, "What is local optimality in nonconvex-nonconcaveminimax optimization?," in Proc. Int.Conf.Mach. Learning, 2020, pp. 4880-4889.
N. H. Nguyen and K. Dogançay, "Improved pseudolinear kalman filter algorithms for bearings-only target tracking," IEEE Trans. Signal Process., vol. 65, no. 23, pp. 6119-6134, Dec. 2017.
K.Dogançay andG. Ibal, "Instrumental variable estimator for3Dbearingsonly emitter localization," in Proc. Int. Conf. Intell. Sensors, Sensor Netw. Inf. Process., 2005, pp. 63-68.
P. Tichavsky, C. H. Muravchik, and A. Nehorai, "Posterior Cramér-Rao bounds for discrete-time nonlinear filtering," IEEE Trans. Signal Process., vol. 46, no. 5, pp. 1386-1396, May 1998.