Abstract
A semidefinite relaxation (SDR) algorithm is proposed for scenarios in which sources, such as locator beacons and marine mammals, transmit signals continuously at multiple locations. In these scenarios, multiple groups of the time-difference-of-arrival (TDOA) measurements can be obtained, and each group of the TDOA measurements corresponds to one source location. The proposed algorithm adds constraints on the distances between the source locations and jointly locates the positions of the source using multiple groups of the TDOA measurements. The objective function of the maximum likelihood (ML) localization estimation is nonconvex, and the SDR is adopted to approximate the nonconvex ML optimization by relaxing it to a semidefinite programming (SDP) problem. The simulation results show the superior performance of the proposed method.
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References
Chan, Y.T., Ho, K.C.: A simple and efficient estimator for hyperbolic location. IEEE Trans. Sig. Process. 42(8), 1905–1915 (1994)
Spirito, M.A.: On the accuracy of cellular mobile station location estimation. IEEE Trans. Veh. Technol. 50(3), 674–685 (2001)
Chan, Y., Hang, H., Ching, P.: Exact and approximate maximum likelihood localization algorithms. IEEE Trans. Veh. Technol. 55(1), 10–16 (2006)
Nesterov, Y.: Lectures on Convex Optimization. Springer Optimization and Its Applications. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-91578-4
Wang, G., Li, Y., Ansari, N.: A semidefinite relaxation method for source localization using TDOA and FDOA measurements. IEEE Trans. Veh. Technol. 62(2), 853–862 (2013)
Wang, Y., Wu, Y.: An efficient semidefinite relaxation algorithm for moving source localization using TDOA and FDOA measurements. IEEE Commun. Lett. 21(1), 80–83 (2017)
Wang, G., So, A.M., Li, Y.: Robust convex approximation methods for TDOA-based localization under NLOS conditions. IEEE Trans. Sig. Process. 64(13), 3281–3296 (2016)
Zou, Y., Liu, H., Wan, Q.: Joint synchronization and localization in wireless sensor networks using semidefinite programming. IEEE Internet Things J. 5(1), 199–205 (2018)
Skarsoulis, E.K., Dosso, S.E.: Linearized two-hydrophone localization of a pulsed acoustic source in the presence of refraction: theory and simulations. J. Acoust. Soc. Am. 138(4), 2221–2234 (2015)
Tran, D.D., et al.: Using a coherent hydrophone array for observing sperm whale range, classification, and shallow-water dive profiles. J. Acoust. Soc. Am. 135(6), 3352–3363 (2014)
Luo, W., Yang, W., Zhang, Y.: Convolutional neural network for detecting odontocete echolocation clicks. J. Acoust. Soc. Am. 145(1), EL7–EL12 (2019)
Yang, W., Luo, W., Zhang, Y.: Classification of odontocete echolocation clicks using convolutional neural network. J. Acoust. Soc. Am. 147(1), 49–55 (2020)
Rideout, B.P., Dosso, S.E., Hannay, D.E.: Underwater passive acoustic localization of Pacific walruses in the northeastern Chukchi Sea. J. Acoust. Soc. Am. 134(3), 2534–2545 (2013)
Barlow, J., Griffiths, E.T., Klinck, H., Harris, D.V.: Diving behavior of Cuvier’s beaked whales inferred from three-dimensional acoustic localization and tracking using a nested array of drifting hydrophone recorders. J. Acoust. Soc. Am. 144(4), 2030–2041 (2018)
Gorman, J., Hero, A.: Lower bounds for parametric estimation with constraints. IEEE Trans. Inform. Theory 26(6), 1285–1301 (1990)
Luo, Z.Q., Ma, W.K., So, A.M.C., Ye, Y., Zhang, S.: Semidefinite relaxation of quadratic optimization problems. IEEE Sig. Process. Mag. 27(3), 20–34 (2010)
CVX Research: CVX: Matlab software for disciplined convex programming, version 2.2. http://cvxr.com/cvx. Accessed 31 Jan 2020
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Zhang, T., Yang, W., Zhang, Y. (2022). Semidefinite Relaxation Algorithm for Source Localization Using Multiple Groups of TDOA Measurements with Distance Constraints. In: Huang, DS., Jo, KH., Jing, J., Premaratne, P., Bevilacqua, V., Hussain, A. (eds) Intelligent Computing Theories and Application. ICIC 2022. Lecture Notes in Computer Science, vol 13393. Springer, Cham. https://doi.org/10.1007/978-3-031-13870-6_19
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DOI: https://doi.org/10.1007/978-3-031-13870-6_19
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