Optimal Sensor Placement for Source Localization: A Unified ADMM Approach

[en] Source localization plays a key role in many applications including radar, wireless and underwater communications. Among various localization methods, the most popular ones are Time-Of-Arrival (TOA), Time-Difference-Of-Arrival (TDOA), Angle-Of-Arrival (AOA) and Received Signal Strength (RSS) based. Since the Cramér-Rao lower bounds (CRLB) of these methods depend on the sensor geometry explicitly, sensor placement becomes a crucial issue in source localization applications. In this paper, we consider finding the optimal sensor placements for the TOA, TDOA, AOA and RSS based localization scenarios. We first unify the three localization models by a generalized problem formulation based on the CRLB-related metric. Then a u nified op t imization fra m ework for o ptimal s ensor placemen t (UTMOST) is developed through the combination of the alternating direction method of multipliers (ADMM) and majorization-minimization (MM) techniques. Unlike the majority of the state-of-the-art works, the proposed UTMOST neither approximates the design criterion nor considers only uncorrelated noise in the measurements. It can readily adapt to to different design criteria (i.e. A, D and E-optimality) with slight modifications within the framework and yield the optimal sensor placements correspondingly. Extensive numerical experiments are performed to exhibit the efficacy and flexibility of the proposed framework.

Disciplines :

Computer science

Author, co-author :

Sahu, Nitesh

Wu, Linlong

Babu, Prabhu

Mysore Rama Rao, Bhavani Shankar ; University of Luxembourg > Interdisciplinary Centre for Security, Reliability and Trust (SNT) > SPARC

Ottersten, Björn ; University of Luxembourg > Interdisciplinary Centre for Security, Reliability and Trust (SNT)

External co-authors :

yes

Language :

English

Title :

Optimal Sensor Placement for Source Localization: A Unified ADMM Approach

Publication date :

2022

Journal title :

IEEE Transactions on Vehicular Technology

ISSN :

0018-9545

Publisher :

IEEE, United States

Volume :

Issue :

Pages :

4359 - 4372

Peer reviewed :

Peer Reviewed verified by ORBi

Focus Area :

Security, Reliability and Trust

Available on ORBilu :

since 27 December 2022

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Bibliography

I. F. Akyildiz, W. Su, Y. Sankarasubramaniam, and E. Cayirci, "A survey on sensor networks, " IEEE Commun. Mag., vol. 40, no. 8, pp. 102-114, Aug. 2002.
D. Li, K. D.Wong, Y. H. Hu, and A. M. Sayeed, "Detection, classification, and tracking of targets, " IEEE Signal Process. Mag., vol. 19, no. 2, pp. 17-29, Mar. 2002.
J. Shen, A. F. Molisch, and J. Salmi, "Accurate passive location estimation using TOAmeasurements, " IEEE Trans.Wireless Commun., vol. 11, no. 6, pp. 2182-2192, Jun. 2012.
Y. Zhu, D. Huang, and A. Jiang, "Network localization using angle of arrival, " in Proc. IEEE Int. Conf. Electro/Inf. Technol., 2008, pp. 205-210.
B. Huang, L. Xie, and Z. Yang, "TDOA-based source localization with distance-dependent noises, " IEEE Trans.WirelessCommun., vol. 14, no. 1, pp. 468-480, Jan. 2015.
A. J. Weiss, "On the accuracy of a cellular location system based on RSS measurements, " IEEE Trans. Veh. Technol., vol. 52, no. 6, pp. 1508-1518, Nov. 2003.
K. Ho and W. Xu, "An accurate algebraic solution for moving source location using TDOA and FDOA measurements, " IEEE Trans. Signal Process., vol. 52, no. 9, pp. 2453-2463, Sep. 2004.
K. Yoo, J. Chun, and C. Ryu, "CRB-based optimal radar placement for target positioning, " in Proc. Int. Conf. Radar, 2018, pp. 1-5.
K.Yoo and J.Chun, "Analysis of optimal range sensor placement for tracking a moving target, " IEEE Commun. Lett., vol. 24, no. 8, pp. 1700-1704, Aug. 2020.
D. Ucinski, Optimal Measurement Methods for Distributed Parameter System Identification. Boca Raton, FL, USA: CRC press, 2004.
K. Dogançay and H. Hmam, "Optimal angular sensor separation for AOA localization, " Signal Process., vol. 88, no. 5, pp. 1248-1260, 2008.
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.
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.
M. Hamdollahzadeh, R. Amiri, and F. Behnia, "Optimal sensor placement for multi-source AOA localisation with distance-dependent noise model, " IET Radar, Sonar Navigation, vol. 13, no. 6, pp. 881-891, 2019.
X. Fang and J. Li, "Frame theory for optimal sensor augmentation problem of AOA localization, " IEEE Signal Process. Lett., vol. 25, no. 9, pp. 1310-1314, Sep. 2018.
Y. Zheng, J. Liu, M. Sheng, S. Han, Y. Shi, and S.Valaee, "Toward practical access point deployment for angle-of-Arrival based localization, " IEEE Trans. Commun., vol. 69, no. 3, pp. 2002-2014, Mar. 2021.
S. Zhao, B. M. Chen, and T. H. Lee, "Optimal sensor placement for target localisation and tracking in 2D and 3D, " Int. J. Control, vol. 86, no. 10, pp. 1687-1704, 2013.
B. Yang and J. Scheuing, "Cramer-rao bound and optimum sensor array for source localization from time differences of arrival, " in Proc. IEEE Int. Conf. Acoust., Speech, Signal Process., 2005, vol. 4, pp. iv/961-iv/964.
W. Meng, L. Xie, and W. Xiao, "Optimal TDOA sensor-pair placement with uncertainty in source location, " IEEE Trans. Veh. Technol., vol. 65, no. 11, pp. 9260-9271, Nov. 2016.
S. Xu, Y. Ou, and X. Wu, "Optimal sensor placement for 3D time-ofarrival target localization, " IEEE Trans. Signal Process., vol. 67, no. 19, pp. 5018-5031, Oct. 2019.
S. Xu, Y. Ou, and W. Zheng, "Optimal sensor-Target geometries for 3D static target localization using received-signal-strength measurements, " IEEE Signal Process. Lett., vol. 26, no. 7, pp. 966-970, Jul. 2019.
L. Rui and K. Ho, "Elliptic localization: Performance study and optimum receiver placement, " IEEE Trans. Signal Process., vol. 62, no. 18, pp. 4673-4688, Sep. 2014.
N. H. Nguyen, "Optimal geometry analysis for target localization with bayesian priors, " IEEE Access, vol. 9, pp. 33 419-33 437, 2021.
A. Heydari, M. Aghabozorgi, and M. Biguesh, "Optimal sensor placement for source localization based on RSSD, " Wireless Netw., vol. 26, no. 7, pp. 5151-5162, 2020.
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.
N. H. Nguyen and K. Dogançay, "Optimal sensor placement for doppler shift target localization, " in Proc. IEEE Radar Conf., 2015, pp. 1677-1682.
S. P. Robinson, P. A. Lepper, and R. A. Hazelwood, "Good practice guide for underwater noise measurement, " Nat. Meas. Office, Marine Scotland, Crown Estate, Teddington, U.K., Tech. Rep. 133, 2014.
S. Joshi and S. Boyd, "Sensor selection via convex optimization, " IEEE Trans. Signal Process., vol. 57, no. 2, pp. 451-462, Feb. 2009.
H. C. So and L. Lin, "Linear least squares approach for accurate received signal strength based source localization, " IEEE Trans. signal Process., vol. 59, no. 8, pp. 4035-4040, Aug. 2011.
S. P. Chepuri and G. Leus, "Sparsity-promoting sensor selection for nonlinear measurement models, " IEEE Trans. Signal Process., vol. 63, no. 3, pp. 684-698, Feb. 2015.
P. Stoica and P. Babu, "The gaussian data assumption leads to the largest cramér-rao bound [lecture notes], " IEEE Signal Process. Mag., vol. 28, no. 3, pp. 132-133, May 2011.
S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory. Englewood Cliffs, NJ, USA: Prentice-Hall, Inc., 1993.
H.-L. Song, "Automatic vehicle location in cellular communications systems, " IEEE Trans. Veh. Technol., vol. 43, no. 4, pp. 902-908, Nov. 1994.
N. Patwari, A. O. Hero, M. Perkins, N. S. Correal, and R. J. O'dea, "Relative location estimation in wireless sensor networks, " IEEE Trans. signal Process., vol. 51, no. 8, pp. 2137-2148, Aug. 2003.
P. Tarrio, A. M. Bernardos, J. A. Besada, and J. R. Casar, "A new positioning technique for RSS-based localization based on a weighted least squares estimator, " in Proc. IEEE Int. Symp.Wireless Commun. Syst., 2008, pp. 633-637.
T. S. Rappaport et al., Wireless Communications: Principles and Practice, vol. 2. Englewood Cliffs, NJ, USA: Prentice Hall PTR, 1996.
A. Atkinson, A. Donev, and R. Tobias, Optimum Experimental Designs, With SAS, vol. 34. New York, NY, USA: Oxford Univ. Press, 2007.
L. Pronzato and A. Pázman, Design of Experiments in Nonlinear Models, (Lecture Notes Statist.), New York, NY, USA: SpringerVerlag, vol. 212, 2013.
S. Boyd, N. Parikh, and E. Chu, "Distributed optimization and statistical learning via the alternating direction method of multipliers, " Foundations Trends Machine Learn., vol. 3, no. 1, pp. 1-122, 2010.
L. Wu and D. P. Palomar, "Sequence design for spectral shaping via minimization of regularized spectral level ratio, " IEEE Trans. Signal Process., vol. 67, no. 18, pp. 4683-4695, Sep. 2019.
T. Wei, L. Wu, and M. Shankar, "Sparse array beampattern synthesis via majorization based ADMM, " in Proc. IEEE Veh. Technol. Conf. (VTC Fall), Sep. 2021, pp. 1-5.
Y. Sun, P. Babu, and D. P. Palomar, "Majorization-minimization algorithms in signal processing, communications, and machine learning, " IEEE Trans. Signal Process., vol. 65, no. 3, pp. 794-816, Feb. 2017.
M. C. Grant and S. P. Boyd, "The cvx users' guide release 2.0 (beta), " CVX Res., Inc, Mar. 2013. [Online]. Available: http://cvxr.com/cvx/doc/CVX.pdf
Y.Wang, W. Yin, and J. Zeng, "Global convergence ofADMMin nonconvex nonsmooth optimization, " J. Sci. Comput., vol. 78, no. 1, pp. 29-63, 2019.
Q. Liu, X. Shen, andY. Gu, "LinearizedADMMfor nonconvex nonsmooth optimization with convergence analysis, " IEEE Access, vol. 7, pp. 76 131-76 144, 2019.
M. Hong, Z.-Q. Luo, and M. Razaviyayn, "Convergence analysis of alternating direction method of multipliers for a family of nonconvex problems, " SIAM J. Optim., vol. 26, no. 1, pp. 337-364, 2016.
M. Razaviyayn, M. Hong, and Z.-Q. Luo, "A unified convergence analysis of block successive minimization methods for nonsmooth optimization, " SIAM J. Optim., vol. 23, no. 2, pp. 1126-1153, 2013.
J. Neering, C. Fischer, M. Bordier, and N. Maizi, "Optimal sensor configuration for passive position estimation, " in Proc. IEEE/ION PLANS, 2008, pp. 951-960.
K. Dogancay andG. Ibal, "Instrumental variable estimator for3Dbearingsonly emitter localization, " in Proc. IEEE Int. Conf. Intell. Sensors, Sensor Netw. Inf. Process., 2005, pp. 63-68.