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Proposed Distributed Kalman Filter

Chapter
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Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 118)

Abstract

In this chapter, the DKF problem is addressed by reducing it into a dynamic consensus problem in term of weighted average estimates matrix that can be viewed as data fusion problem. We have presented a Distributed Kalman Filter based on polynomial filter to accelerate the distributed average consensus in the static network topologies. The proposed algorithm performs closely to the central filter, and also reduces the filter complexity at each node by reducing the dimension of the data. Thus, it scales computational complexity. Being based on sending only the estimates between neighbors, it also reduced radically the communication requirements. The proposed DKF contributes to significant energy saving.

Keywords

Sensor Network Sensor Node Convergence Rate Wireless Sensor Network Kalman Filter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Bibliography

  1. 1.
    N.T. John and A. Michael, “Convergence and asymptotic agreement in distributed decision problems,” in Proceeding of the 21st IEEE Conference on Decision and Control, Orlando, Florida, USA, December 1982, pp. 692–701.Google Scholar
  2. 2.
    R. Wei and R.W. Beard, “Consensus seeking in multiagent systems under dynamically changing interaction topologies,” IEEE Transactions on Automatic Control, vol. 50, pp. 655–661, November 2005.CrossRefGoogle Scholar
  3. 3.
    L. Xiao, S. Boyd, and S. Lall, “A scheme for robust distributed sensor fusion based on average consensus,” in the 4th International Symposium onInformation Processing in Sensor Networks, pp. 63–70, 2005.Google Scholar
  4. 4.
    C.C. Moallemi and B. Van Roy, “Consensus Propagation,” IEEE Transactions on Information Theory, vol. 52, pp. 4753–4766, January 2006.CrossRefGoogle Scholar
  5. 5.
    D. Spanos, R. Olfati-Saber, and R. Murray, “Distributed sensor fusion using dynamic consensus,” in Proceeding of the 16th IFAC World Congress, Prague, Czech Republic, July 2005, pp. 199–205.Google Scholar
  6. 6.
    D.S. Scherber and H.C. Papadopoulos, “Locally constructed algorithms for distributed computations in ad-hoc networks,” in Proceeding of the 3rd International Symposium on Information Processing in Sensor Networks, Berkeley, California, USA, April 2004, pp. 11–19.Google Scholar
  7. 7.
    L. Xiao, S. Boyd, and S.J. Kim, “Distributed average consensus with least-mean-square deviation,” in Proceeding of the 17th International Symposium on Mathematical Theory of Networks and Systems, Kyoto, Japan, July 2006, pp. 2768–2776.Google Scholar
  8. 8.
    L. Xiao, S. Boyd, and S.-J. Kim, “Distributed average consensus with least–mean–square deviation,” Journal of Parallel and Distributed Computing, vol. 2, pp. 33–46, May 2007.CrossRefGoogle Scholar
  9. 9.
    L. Xiao and S. Boyd, “Fast linear iterations for distributed averaging,” Systems and Control Letters, pp. 65–78, June 2004.Google Scholar
  10. 10.
    R. Olfati-Saber and R.M. Murray, “Consensus problems in networks of agents with switching topology and time-delays,” IEEE Transactions on Automatic Control, vol. 49, pp. 1520–1533, January 2004.MathSciNetCrossRefGoogle Scholar
  11. 11.
    S. Boyd, A. Ghosh, B. Prabhakar, and D. Shah, “Randomized gossip algorithms,” IEEE Transactions on Information Theory, vol. 52, pp. 2508–2530, June 2006.MathSciNetCrossRefGoogle Scholar
  12. 12.
    S. Sundaram, “Distributed Consensus and Linear Functional Calculation in Networks: An Observability Perspective,” in Proceeding of the 6th International Symposium on Information Processing in Sensor Networks, Cambridge, Massachusetts, USA, April 2007, pp. 99–108.Google Scholar
  13. 13.
    J. Liu, B.D.O. Anderson, M. Cao, and A.S. Morse, “Analysis of accelerated gossip algorithms,” in Proceeding of the 48th IEEE Conference on Decision and Control, Chinghai, China, December 2009, pp. 871–876.Google Scholar
  14. 14.
    J. Dong, Q. Chen, and Z. Niu, “Random graph theory based connectivity analysis in wireless sensor networks with Rayleigh fading channels,” in Proceeding of the Asia-Pacific Conference on Communications, Hong Kong, China, March 2007, pp. 123–126.Google Scholar
  15. 15.
    B. Bollabas, Random Graphs Second Edition: Cambride University Press, 2001.Google Scholar
  16. 16.
    E. Kokiopoulou and P. Frossard, “Polynomial Filtering for Fast Convergence in Distributed Consensus,” IEEE Transactions on Signal Processing, vol. 57, pp. 342–354, October 2009.MathSciNetCrossRefGoogle Scholar
  17. 17.
    S. Kar and J.M.F. Moura, “Sensor Networks With Random Links: Topology Design for Distributed Consensus,” IEEE Transactions on Signal Processing, vol. 56, pp. 3315–3326, March 2008.MathSciNetCrossRefGoogle Scholar
  18. 18.
    R. Olfati-Saber, “Distributed Kalman Filter with Embedded Consensus Filters,” in the 44th IEEE Conference on Decision and Control, pp. 8179–8184, 2005.Google Scholar
  19. 19.
    A. Abdelgawad and M. Bayoumi, “Low Power Distributed Kalman Filter for Wireless Sensor Networks,” EURASIP Journal on Embedded Systems, vol. 2011, Article ID 693150, 11 pages, doi: 10.1155/2011/693150, 2011.
  20. 20.
    A. Abdelgawad and M. Bayoumi,“ Distributed Kalman Filter Using Fast Polynomial Filter,” IEEE International Symposium on Circuits and Systems, ISCAS 2011, 15–18 May 2011Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Essex JunctionUSA
  2. 2.University of Louisiana at LafayetteLafayetteUSA

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