Skip to main content

Fourier Density Approximation for Belief Propagation in Wireless Sensor Networks

  • Chapter
  • First Online:
Multisensor Fusion and Integration for Intelligent Systems

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 35))

  • 1439 Accesses

Abstract

Many distributed inference problems in wireless sensor networks can be represented by probabilistic graphical models, where belief propagation, an iterative message passing algorithm provides a promising solution. In order to make the algorithm efficient and accurate, messages which carry the belief information from one node to the others should be formulated in an appropriate format. This paper presents two belief propagation algorithms where non-linear and non-Gaussian beliefs are approximated by Fourier density approximations, which significantly reduces power consumptions in the belief computation and transmission. We use self-localization in wireless sensor networks as an example to illustrate the performance of this method.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Refernece

  1. Gharavi, H., Kumar, S. (Eds.): Special issue on sensor networks and applications. In Proceedings of the IEEE, vol.91, no.8, Aug. 2003

    Google Scholar 

  2. Kumar, S., Zhao, F., Shepherd, D. (Eds.): Special issue on collaborative information processing. In IEEE Signal Processing Magazine, vol.19, no.2, Mar. 2002

    Google Scholar 

  3. Ihler, A., Fisher, J., Moses, R., Willsky, A.: Nonparametric belief propagation for self-calibration in sensor networks. In Proceedings of IPSN 2004

    Google Scholar 

  4. Kronmal, R., Tarter, M.: The estimation of probability densities and cumulatives by Fourier series methods. In Journal of the American Statistical Association, vol.63, no.323, pp.925–952, Sep. 1968

    Google Scholar 

  5. Brunn, D., Sawo, F., Hanebeck, U.D.: Efficient nonlinear Bayesian estimation based on Fourier densities. In Proceedings of the 2006 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI 2006), Germany 2006

    Google Scholar 

  6. Brunn, D., Sawo, F., Hanebeck, U.D.: Nonlinear multidimensional Bayesian estimation with Fourier densities. In Proceedings of the 2006 IEEE Conference on Decision and Control (CDC 2006), pp.1303–1308, San Diego, California, Dec. 2006

    Google Scholar 

  7. Lauritzen, S.L.: Graphical Models. Oxford University Press, Oxford, 1996

    Google Scholar 

  8. Clifford, P.: Markov random fields in statistics. In Grimmett, G.R., Welsh, D.J.A. (Eds.) Disorder in Physical Systems, pp.19C32. Oxford University Press, Oxford, 1990

    Google Scholar 

  9. Paskin, M., Guestrin, C.: A robust architecture for distributed inference in sensor networks. Intel Research, Technical Report IRB-TR-03-039, 2004.

    Google Scholar 

  10. Aji, S.M., McEliece, R.J.: The generalized distributive law. IEEE Transactions on Information Theory vol.46, pp.325–343, Mar. 2000

    Google Scholar 

  11. Murphy, K., Weiss, Y., Jordan, M.: Loopy-belief propagation for approximate inference: An empirical study. In Uncertainty in Artificial Intelligence vol.15, pp.467–475, Jul. 1999

    Google Scholar 

  12. Kschischang, F.R., Frey, B.J., Loeliger, H.A.: Factor graph and the sum-product algorithm. IEEE Transactions Information Theory, vol.47, no.2, pp.498–518, Feb. 2001.

    Google Scholar 

  13. Hanebeck, U.D.: Progressive Bayesian estimation for nonlinear discrete-time systems: the measurement step. In Proceedings of the 2003 IEEE Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI 2003), pp.173–178, Tokyo, Japan, Jul. 2003.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Chongning Na .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Na, C., Wang, H., Obradovic, D., Hanebeck, U.D. (2009). Fourier Density Approximation for Belief Propagation in Wireless Sensor Networks. In: Hahn, H., Ko, H., Lee, S. (eds) Multisensor Fusion and Integration for Intelligent Systems. Lecture Notes in Electrical Engineering, vol 35. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89859-7_25

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-89859-7_25

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-89858-0

  • Online ISBN: 978-3-540-89859-7

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics