Robust Modified Newton Algorithms Using Tikhonov Regularization for TDOA Source Localization

  • Jiaqi FangEmail author
  • Zhiyi He
Short Paper


This paper addresses a modified Newton (MNT) algorithm for the source localization problem utilizing time difference of arrival. As the improvement of the Newton (NT) method, the proposed algorithm can guarantee convergence stability in the case of bad initial values by using the Tikhonov (TI) regularization theory. Moreover, a two-stage MNT algorithm is proposed for the source localization with sensor position errors. Theoretical analysis is provided to illustrate that the two-stage MNT algorithm has less computational load and faster convergence speed compared with the MNT algorithm. Simulation results show the superior location accuracy and better convergence performance of the proposed MNT and two-stage MNT algorithms in comparison with relative methods.


Source localization Time difference of arrival (TDOA) Modified Newton method (MNT) Tikhonov (TI) regularization theory Two-stage MNT method Sensor position errors 



This work was supported in part by the National Natural Science Foundation of China under Grants 61801363.


  1. 1.
    R.J. Barton, D. Rao, Performance capabilities of long-range UWB-IR TDOA localization systems. EURASIP J. Adv. Signal Process. 2008(1), 236791 (2008)zbMATHGoogle Scholar
  2. 2.
    D. Calvetti, S. Morigi, L. Reichel et al., Tikhonov regularization and the L-curve for large discrete ill-posed problems. J. Comput. Appl. Math. 123(1), 423–446 (2000)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Y.T. Chan, K.C. Ho, A simple and efficient estimator for hyperbolic location. IEEE Trans. Signal Process. 42(8), 1905–1915 (2002)Google Scholar
  4. 4.
    N.G. Chernoguz, A smoothed Newton–Gauss method with application to bearing-only position location. IEEE Trans. Signal Process. 43(8), 2011–2013 (1995)Google Scholar
  5. 5.
    K.W. Cheung, H.C. So, W.K. Ma et al., A constrained least squares approach to mobile positioning: algorithms and optimality. EURASIP J. Adv. Signal Process. 2006(1), 020858 (2006)Google Scholar
  6. 6.
    W.H. Foy, Position-location solutions by Taylor-series estimation. IEEE Trans. Aerosp. Electron. Syst. 12(2), 187–194 (2007)Google Scholar
  7. 7.
    B. Friedlander, A passive localization algorithm and its accuracy analysis. IEEE J. Ocean. Eng. 12(1), 234–245 (1987)Google Scholar
  8. 8.
    T.T. Ha, R.C. Robertson, Geostationary satellite navigation systems. IEEE Trans. Aerosp. Electron. Syst. AES- 23(2), 247–254 (1987)Google Scholar
  9. 9.
    P.C. Hansen, Regularization tools: a Matlab package for analysis and solution of discrete ill-posed problems. Numer. Algorithms 6(1), 1–35 (1994)MathSciNetzbMATHGoogle Scholar
  10. 10.
    P.C. Hansen, T.K. Jensen, G. Rodriguez, An adaptive pruning algorithm for the discrete L-curve criterion. J. Comput. Appl. Math. 198(2), 483–492 (2015)MathSciNetzbMATHGoogle Scholar
  11. 11.
    K.C. Ho, Bias reduction for an explicit solution of source localization using TDOA. IEEE Trans. Signal Process. 60(5), 2101–2114 (2012)MathSciNetzbMATHGoogle Scholar
  12. 12.
    K.C. Ho, L. Yang, On the use of a calibration emitter for source localization in the presence of sensor position uncertainty. IEEE Trans. Signal Process. 56(12), 5758–5772 (2008)MathSciNetzbMATHGoogle Scholar
  13. 13.
    K.C. Ho, X. Lu, L. Kovavisaruch, Source localization using TDOA and FDOA measurements in the presence of receiver location errors: analysis and solution. IEEE Trans. Signal Process. 55(2), 684–696 (2007)MathSciNetzbMATHGoogle Scholar
  14. 14.
    D.P. O’Leary, P.C. Hansen, The use of the L-curve in the regularization of discrete Ill-posed problems. SIAM J. Sci. Comput. 14(6), 1487–1490 (1993)MathSciNetzbMATHGoogle Scholar
  15. 15.
    A.H. Sayed, Network-based wireless location. IEEE Signal Process. Mag. 22, 24–40 (1996)Google Scholar
  16. 16.
    M. Sun, L. Yang, K.C. Ho, Accurate sequential self-localization of sensor nodes in closed-form. Signal Process. 92(12), 2940–2951 (2012)Google Scholar
  17. 17.
    G. Wang, Y. Li, N. Ansari, A semidefinite relaxation method for source localization using TDOA and FDOA measurements. IEEE Trans. Veh. Technol. 62(2), 853–862 (2013)Google Scholar
  18. 18.
    H.W. Wei, R. Peng, Q. Wan et al., Multidimensional scaling analysis for passive moving target localization with TDOA and FDOA measurements. IEEE Trans. Signal Process. 58(3), 1677–1688 (2010)MathSciNetzbMATHGoogle Scholar
  19. 19.
    E. Weinstein, Optimal source localization and tracking from passive array measurements. IEEE Trans. Acoust. Speech Signal Process. 30(1), 69–76 (2003)Google Scholar
  20. 20.
    Y. Weng, W. Xiao, L. Xie, Total least squares method for robust source localization in sensor networks using TDOA measurements. Int J Distrib. Sensor Netw. 7, 1063–1067 (2011)Google Scholar
  21. 21.
    K. Yang, G. Wang, Z. Luo, Efficient convex relaxation methods for robust target localization by a sensor network using time differences of arrivals. IEEE Trans. Signal Process. 57(7), 2775–2784 (2009)MathSciNetzbMATHGoogle Scholar
  22. 22.
    K. Yang, J. An, X. Bu et al., Constrained total least-squares location algorithm using time-difference-of-arrival measurements. IEEE Trans. Veh. Technol. 59(3), 1558–1562 (2010)Google Scholar
  23. 23.
    H. Yu, G. Huang, J. Gao et al., An efficient constrained weighted least squares algorithm for moving source location using TDOA and FDOA measurements. IEEE Trans. Wirel. Commun. 11(1), 44–47 (2012)Google Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Beijing Institute of Remote Sensing DeviceBeijingPeople’s Republic of China

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