Open Access

Kalman Filters for Time Delay of Arrival-Based Source Localization

  • Ulrich Klee1,
  • Tobias Gehrig1 and
  • John McDonough1
EURASIP Journal on Advances in Signal Processing20062006:012378

Received: 9 February 2005

Accepted: 17 October 2005

Published: 27 March 2006


In this work, we propose an algorithm for acoustic source localization based on time delay of arrival (TDOA) estimation. In earlier work by other authors, an initial closed-form approximation was first used to estimate the true position of the speaker followed by a Kalman filtering stage to smooth the time series of estimates. In the proposed algorithm, this closed-form approximation is eliminated by employing a Kalman filter to directly update the speaker's position estimate based on the observed TDOAs. In particular, the TDOAs comprise the observation associated with an extended Kalman filter whose state corresponds to the speaker's position. We tested our algorithm on a data set consisting of seminars held by actual speakers. Our experiments revealed that the proposed algorithm provides source localization accuracy superior to the standard spherical and linear intersection techniques. Moreover, the proposed algorithm, although relying on an iterative optimization scheme, proved efficient enough for real-time operation.


Authors’ Affiliations

Institut für Theoretische Informatik, Universitäat Karlsruhe


  1. Omologo M, Svaizer P: Acoustic event localization using a crosspower-spectrum phase based technique. Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '94), April 1994, Adelaide, SA, Australia 2: 273-276.Google Scholar
  2. Kay SM: Fundamentals of Statistical Signal Processing: Estimation Theory. Prentice-Hall, Englewood Cliffs, NJ, USA; 1993.MATHGoogle Scholar
  3. Brandstein MS: A framework for speech source localization using sensor arrays, M.S. thesis. Brown University, Providence, RI, USA; 1995.Google Scholar
  4. Brandstein MS, Adcock JE, Silverman HF: A closed-form location estimator for use with room environment microphone arrays. IEEE Transactions on Speech and Audio Processing 1997, 5(1):45-50. 10.1109/89.554268View ArticleGoogle Scholar
  5. Chan YT, Ho KC: A simple and efficient estimator for hyperbolic location. IEEE Transactions on Signal Processing 1994, 42(8):1905-1915. 10.1109/78.301830MathSciNetView ArticleGoogle Scholar
  6. Schau HC, Robinson AZ: Passive source localization employing intersecting spherical surfaces from time-of-arrival differences. IEEE Transactions on Acoustics, Speech, and Signal Processing 1987, 35(8):1223-1225.View ArticleGoogle Scholar
  7. Smith JO, Abel JS: Closed-form least-squares source location estimation from range-difference measurements. IEEE Transactions on Acoustics, Speech, and Signal Processing 1987, 35(12):1661-1669. 10.1109/TASSP.1987.1165089View ArticleGoogle Scholar
  8. Dvorkind TG, Gannot S: Speaker localization exploiting spatial-temporal information. Proceedings of the IEEE International Workshop on Acoustic Echo and Noise Control (IWAENC '03), September 2003, Kyoto, Japan 295-298.Google Scholar
  9. Duraiswami R, Zotkin D, Davis LS: Multimodal 3-D tracking and event detection via the particle filter. Proceedings of IEEE Workshop on Detection and Recognition of Events in Video in Association with IEEE International Conference on Computer Vision, July 2001, Vancouver, BC, Canada 20-27.Google Scholar
  10. Ward DB, Lehmann EA, Williamson RC: Particle filtering algorithms for tracking an acoustic source in a reverberant environment. IEEE Transactions on Speech and Audio Processing 2003, 11(6):826-836. 10.1109/TSA.2003.818112View ArticleGoogle Scholar
  11. Lehmann EA, Ward DB, Williamson RC: Experimental comparison of particle filtering algorithms for acoustic source localization in a reverberant room. Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '03), April 2003, Hong Kong, China 5: 177-180.Google Scholar
  12. Arulampalam MS, Maskell S, Gordon N, Clapp T: A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking. IEEE Transactions on Signal Processing 2002, 50(2):174-188. 10.1109/78.978374View ArticleGoogle Scholar
  13. Hahn WR, Tretter SA: Optimum processing for delay-vector estimation in passive signal arrays. IEEE Transactions on Information Theory 1973, 19(5):608-614. 10.1109/TIT.1973.1055077View ArticleMATHGoogle Scholar
  14. Jazwinski AH: Stochastic Processes and Filtering Theory. Academic Press, New York, NY, USA; 1970.MATHGoogle Scholar
  15. Chen J, Benesty J, Huang YA: Robust time delay estimation exploiting redundancy among multiple microphones. IEEE Transactions on Speech and Audio Processing 2003, 11(6):549-557. 10.1109/TSA.2003.818025View ArticleGoogle Scholar
  16. Huang YA, Benesty J, Elko GW, Mersereati RM: Real-time passive source localization: a practical linear-correction least-squares approach. IEEE Transactions on Speech and Audio Processing 2001, 9(8):943-956. 10.1109/89.966097View ArticleGoogle Scholar
  17. Strobel N, Spors S, Rabenstein R: Joint audio-video signal processing for object localization and tracking. In Microphone Arrays. Edited by: Brandstein M, Ward D. Spinger, Heidelberg, Germany; 2001. chapter 10Google Scholar
  18. Haykin S: Adaptive Filter Theory. 4th edition. Prentice-Hall, Englewood Cliffs, NJ, USA; 2002.MATHGoogle Scholar
  19. Golub GH, Van Loan CF: Matrix Computations. 3rd edition. The Johns Hopkins University Press, Baltimore, Md, USA; 1996.MATHGoogle Scholar
  20. Gehrig T, Nickel K, Ekenel HK, Klee U, McDonough J: Kalman filters for audio-video source localization. Proceedings of IEEE Workshop on Applications of Signal Processing to Audio and Acoustics (WASPAA '05), October 2005, New Paltz, NY, USA 118-121.Google Scholar
  21. Armani L, Matassoni M, Omologo M, Svaizer P: Use of a CSP-based voice activity detector for distant-talking ASR. Proceedings of 8th European Conference on Speech Communication and Technology (EUROSPEECH '03), September 2003, Geneva, Switzerland 2: 501-504.Google Scholar
  22. Bertsekas DP: Nonlinear Programming. Athenea Scientific, Belmont, Mass, USA; 1995.MATHGoogle Scholar
  23. Zhang Z: A flexible new technique for camera calibration. IEEE Transactions on Pattern Analysis and Machine Intelligence 2000, 22(11):1330-1334. 10.1109/34.888718View ArticleGoogle Scholar
  24. Focken D, Stiefelhagen R: Towards vision-based 3-D people tracking in a smart room. Proceedings of 4th IEEE International Conference on Multimodal Interfaces (ICMI '02), October 2002, Pittsburgh, Pa, USA 400-405.View ArticleGoogle Scholar
  25. Abel JS, Smith JO: The spherical interpolation method for closed-form passive source localization using range difference measurements. Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '87), April 1987, Dallas, Tex, USA 12: 471-474.View ArticleGoogle Scholar
  26. Welch GF, Bishop G: SCAAT: incremental tracking with incomplete information. Proceedings of 24th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH '97), August 1997, Los Angeles, Calif, USA 333-344.View ArticleGoogle Scholar
  27. Welch GF: SCAAT: incremental tracking with incomplete information, M.S. thesis. University of North Carolina, Chapel Hill, NC, USA; 1996.Google Scholar
  28. Sayed AH, Kailath T: A state-space approach to adaptive RLS filtering. IEEE Signal Processing Magazine 1994, 11(3):18-60. 10.1109/79.295229MathSciNetView ArticleGoogle Scholar
  29. McDonough J, Klee U, Gehrig T: Kalman filtering for time delay of arrival-based source localization. In Tech. Rep. 104. Interactive Systems Laboratories, Universität Karlsruhe, Karlsruhe, Germany; December 2004.Google Scholar


© Klee et al. 2006