Skip to main content
SpringerLink
Log in

An adaptive tracking algorithm for direction finding and array shape estimation in a nonstationary environment

  • Published:
Journal of VLSI signal processing systems for signal, image and video technology Aims and scope Submit manuscript

Abstract

This paper presents an adaptive tracking algorithm for the subspace-based direction of arrival estimation of multiple sources in a nonstationary, environment. The nonstationarities are due to moving sources or to timevarying distortions of the sensor array shape. The proposed algorithm relies on the properties of a linear operator, referred to as the Propagator, which only exploits the linear independency of the source steering vectors. The Propagator allows not only the calibration of the array shape, but also the determination of the source and the noise subspaces without any eigendecomposition of the cross-spectral matrix of the received signals. A gradientbased adaptive algorithm is here proposed for the on-line estimation of the Propagator. A theoretical analysis of the behaviour of this algorithm in a nonstationary environment is given. Simulations are carried out in the case of moving sources and in the case of a time-varying array shape. They exhibit the good performances of the proposed algorithm.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. G. Bienvenu and L. Kopp, “Optimality of high resolution array processing using the eigensystem approach,”IEEE Trans. Acoust., Speech, Signal Processing Vol. ASSP-31, pp. 1235–1247, Oct. 1983.

    Article  Google Scholar 

  2. R.O. Schmidt, “Multiple emitter location and signal parameters estimation,”Proceedings of the RADC Spectrum Estimation Workshop, Oct. 1979.

  3. J.P. Le Cadre et al., “La calibration d'antenne,”IEEE Traitement du Signal, Special Issue, J.P. Le Cadre (Ed.), Vol. 10, Nos. 5–6, dy1993.

  4. J. Munier and G.Y. Delisle, “Spatial analysis using new properties of the cross-spectral matrix,”IEEE Trans. on Signal Processing, Vol. SP-39, pp. 746–749, March 1991.

    Article  Google Scholar 

  5. S. Marcos and M. Benidir, “On a high resolution array processing method non-based on the eigenanalysis approach,”Proceedings of ICASSP-90, Albuquerque, New Mexico, 1990, pp. 2955–2958.

  6. S. Marcos, “Calibration of a distorted towed array using a propagation operator,”Journal of Acoust. Society of America, Vol. 93, No. 4, pp. 1987–1994, March 1993.

    Article  Google Scholar 

  7. R.D. DeGroat, “Non-iterative subspace tracking,”IEEE Trans. on Acoustics, Speech and Signal Processing, Vol. 40, No. 3, pp. 571–577, March 1992.

    Article  Google Scholar 

  8. R.D. DeGroat and A. Roberts, “Highly parallel eigenvector update algorithms with application to signal processing,”Proceedings of SPIE Int. Soc. Opt. Eng., Vol. 696, pp. 62–70, Aug. 1986.

    Google Scholar 

  9. R. Schreiber, “Implementation of adaptive array algorithms,”IEEE Trans. on ASSP, Vol. ASSP-34, pp. 1038–1045, Oct. 1986.

    Article  MATH  Google Scholar 

  10. C.H. Bischof and G.M. Schroff, “On updating signal subspaces,”IEEE Trans. on Signal Processing, Vol. SP-40, No. 1, pp. 96–105, Jan. 1992, Oct. 1983.

    Article  Google Scholar 

  11. K.C. Sharman, “Adaptive algorithms for estimating the complete covariance eigenstructure,”Proceedings of IEEE Int. Conf. Acoust. SpeechICASSP, pp. 1401–1403, 1986.

  12. G.W. Stewart, “An updating algorithm for subspace tracking,”IEEE Trans. on Acoustics, Speech and Signal Processing, Vol. 40, No. 6, pp. 1535–1541, June 1992.

    Article  Google Scholar 

  13. J.F. Yang and M. Kaveh, “Adaptive eigensubspace algorithms for direction or frequency estimation and tracking,”IEEE Trans. on Acoustics, Speech and Signal Processing, Vol. ASSP-36, pp. 241–251, Feb. 1988.

    Article  Google Scholar 

  14. P. Comon and G.H. Golub, “Tracking a few extreme singular values and vectors in signal processing,”Proceedings of the IEEE, Vo. 78, No. 8, pp. 1327–1343, Aug. 1990.

    Article  Google Scholar 

  15. S. Marcos, A. Marsal, and M. Benidir, “The propagator method for source bearing estimation,”Signal Processing, Vol. 42, No. 2, pp. 121–138, March 1995.

    Article  Google Scholar 

  16. S. Marcos and J. Munier, “Le Propagateur et son estimation adaptative,” Actes du Colloque GRETSI, Juan les Pins, France, Sept. 1989, pp. 489–492.

  17. S. Marcos and O. Macchi, “Tracking capability of the LMS algorithm: Application to an asynchronous echo canceller,”IEEE Trans. on ASSP, Vol. ASSP-35, pp. 1570–1578, Nov. 1987.

    Article  Google Scholar 

  18. B. Yang, “Projection approximation subspace tracking,”IEEE Trans. on Signal Processing, Vol. SP-43, No. 1, pp. 95–107, Jan. 1995.

    Article  MATH  Google Scholar 

  19. A. Eriksson, P. Stoca, and T. Soderstrom, “On-line subspace algorithms for tracking moving sources,”IEEE Trans. on Signal Processing, Vol. SP-42, pp. 2319–2330, Sept. 1994.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Ecole Supérieure d'Electricité, Laboratoire des Signaux et Systèmes, Plateau de Moulon 91192, Gif-sur-Yvette Cedex, France

    Sylvie Marcos, Messaoud Benidir & Javier Sanchez-Araujo

Authors
  1. Sylvie Marcos
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Messaoud Benidir
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Javier Sanchez-Araujo
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Marcos, S., Benidir, M. & Sanchez-Araujo, J. An adaptive tracking algorithm for direction finding and array shape estimation in a nonstationary environment. J VLSI Sign Process Syst Sign Image Video Technol 14, 107–118 (1996). https://doi.org/10.1007/BF00925272

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00925272

Keywords

Search

Navigation