Distributed Approximation and Tracking Using Selective Gossip

  • Deniz Üstebay
  • Rui Castro
  • Mark Coates
  • Michael Rabbat
Part of the Signals and Communication Technology book series (SCT)


This chapter presents selective gossip which is an algorithm that applies the idea of iterative information exchange to vectors of data. Instead of communicating the entire vector and wasting network resources, our method adaptively focuses communication on the most significant entries of the vector. We prove that nodes running selective gossip asymptotically reach consensus on these significant entries, and they simultaneously reach an agreement on the indices of entries which are insignificant. The results demonstrate that selective gossip provides significant communication savings in terms of the number of scalars transmitted. In the second part of the chapter we propose a distributed particle filter employing selective gossip. We show that distributed particle filters employing selective gossip provide comparable results to the centralized bootstrap particle filter while decreasing the communication overhead compared to using randomized gossip to distribute the filter computations.


  1. 1.
    Bénézit F, Dimakis A, Thiran P, Vetterli M (2007) Gossip along the way: Order-optimal consensus through randomized path averaging. In: Proceedings of the Allerton Conference on Communication, Control, and Computing, MonticelloGoogle Scholar
  2. 2.
    Bertsekas DP, Tsitsiklis JN (1997) Parallel and distributed computation: Numerical methods. Athena Scientific, BelmontGoogle Scholar
  3. 3.
    Boyd S, Ghosh A, Prabhakar B, Shah D (2006) Randomized gossip algorithms. IEEE Trans Info Theory 52(6):2508–2530MathSciNetCrossRefGoogle Scholar
  4. 4.
    Cappé O, Moulines E, Ryden T (2005) Inference in hidden Markov models. Springer-Verlag, New YorkMATHGoogle Scholar
  5. 5.
    Coates M (2004) Distributed particle filters for sensor networks. In: Proceedings of the International Symposium on Information Processing in Sensor Networks (IPSN), BerkeleyGoogle Scholar
  6. 6.
    Dimakis A, Sarwate A, Wainwright M (2006) Geographic gossip: Efficient aggregation for sensor networks. In: Proceedings of the International Conference on Information Processing in Sensor Networks (IPSN), NashvilleGoogle Scholar
  7. 7.
    Dimakis AG, Kar S, Moura JMF, Rabbat MG, Scaglione A (2010) Gossip algorithms for distributed signal processing. Proc IEEE 98(11):1847–1864CrossRefGoogle Scholar
  8. 8.
    Doucet A, de Freitas N, Gordon N (eds) (2001) Sequential Monte Carlo methods in practice. Springer-Verlag, New YorkGoogle Scholar
  9. 9.
    Doucet A, Johansen M (2010) Oxford handbook of nonlinear filtering, chapter A tutorial on particle filtering and smoothing: fifteen years later. Oxford University Press, to appearGoogle Scholar
  10. 10.
    Farahmand S, Roumeliotis SI, Giannakis GB (2011) Set-membership constrained particle filter: Distributed adaptation for sensor networks. IEEE Trans Signal Process 59(9):4122–4138Google Scholar
  11. 11.
    Gordon NJ, Salmond DJ, Smith AFM (1993) Novel approach to nonlinear/non-Gaussian Bayesian state estimation. IEE Proc-F 140(2):107–113Google Scholar
  12. 12.
    Grimmett GR, Stirzaker DR (2001) Probability and random processes. Oxford University Press, New YorkGoogle Scholar
  13. 13.
    Gu D (2007) Distributed particle filter for target tracking. In: Proceedings IEEE International Conference on Robotics and Automation, RomeGoogle Scholar
  14. 14.
    Gupta P, Kumar PR (2000) The capacity of wireless networks. IEEE Trans Info Theory 46(2):388–404MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Handschin JE, Mayne DQ (1969) Monte Carlo techniques to estimate the conditional expectation in multi-stage non-linear filtering. Int J Control 9(5):547–559MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Hendrickx JM, Tsitsiklis JN (2011) Convergence of type-symmetric and cut-balanced consensus seeking systems. Submitted; available at
  17. 17.
    Hlinka O, Sluciak O, Hlawatsch F, Djurić PM, Rupp M (2010) Likelihood consensus: Principles and application to distributed particle filtering. In: The forty fourth Asilomar Conference on Signals, Systems and Computers (ASILOMAR)Google Scholar
  18. 18.
    Jadbabaie A, Lin J, Morse AS (2003) Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans Autom Control 48(6):988–1001Google Scholar
  19. 19.
    Kokiopoulou E, Frossard P (2009) Polynomial filtering for fast convergence in distributed consensus. IEEE Trans Signal Process 57(1):342–354MathSciNetCrossRefGoogle Scholar
  20. 20.
    Lee SH, West M (2009) Markov chain distributed particle filters (MCDPF). In: Proceedings of the IEEE Conference on Decision and Control, ShanghaiGoogle Scholar
  21. 21.
    Mohammadi A, Asif A (2011) Consensus-based distributed unscented particle filter.In: Proceedings of the IEEE Statistical Signal Processing Workshop (SSP), 237–240Google Scholar
  22. 22.
    Nedić A, Ozdaglar A (2009) Distributed subgradient methods for multi-agent optimization. IEEE Trans Autom Control 54(1):48–61CrossRefGoogle Scholar
  23. 23.
    Olfati-Saber R, Fax JA, Murray RM (2007) Consensus and cooperation in networked multi-agent systems. Proc IEEE 95(1):215–233CrossRefGoogle Scholar
  24. 24.
    Oreshkin BN, Coates MJ, Rabbat MG (2010) Optimization and analysis of distributed averaging with short node memory. IEEE Trans Signal Process 58(5):2850–2865MathSciNetCrossRefGoogle Scholar
  25. 25.
    Oreshkin BN, Coates MJ (2010) Asynchronous distributed particle filter via decentralized evaluation of Gaussian products. In: Proceedings of the ISIF International Conference on Information Fusion, EdinburghGoogle Scholar
  26. 26.
    Rabbat M, Nowak R, Bucklew J (2005) Robust decentralized source localization via averaging In: Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP). PhiladelphiaGoogle Scholar
  27. 27.
    Ristic B, Arulampalam MS (2003) Tracking a manoeuvring target using angle-only measurements: algorithms and performance. Signal Process 83(6):1223–1238CrossRefMATHGoogle Scholar
  28. 28.
    Ristic B, Arulampalam S, Gordon N (2004) Beyond the Kalman filter: particle filters for tracking applications. Artech House, Norwood, MA, USAGoogle Scholar
  29. 29.
    Sheng X, Hu Y-H, Ramanathan P (2005) Distributed particle filter with GMM approximation for multiple targets localization and tracking in wireless sensor network. In: Proceedings of the International Symposium on Information Processing in Sensor Networks (IPSN), Los AngelesGoogle Scholar
  30. 30.
    Sundhar Ram S, Veeravalli VV, Nedić A (2010) Distributed and recursive parameter estimation in parametrized linear state-space models. IEEE Trans Autom Control 55(2):488–492CrossRefGoogle Scholar
  31. 31.
    Touri B (2011) Product of random stochastic matrices and distributed averaging. PhD thesis, Univeristy of Illinois at Urbana-ChampaignGoogle Scholar
  32. 32.
    Tsitsiklis JN (1984) Problems in decentralized decision making and computation. PhD Thesis, MITGoogle Scholar
  33. 33.
    Tsitsiklis JN, Bertsekas DP, Athans M (1986) Distributed asynchronous deterministic and stochastic gradient optimization algorithms. IEEE Trans Autom Control 31(9):803–812MathSciNetCrossRefMATHGoogle Scholar
  34. 34.
    Üstebay D, Castro R, Rabbat M (2011) Efficient decentralized approximation via selective gossip. IEEE J Sel Top Sign Proc 5(4):805–816CrossRefGoogle Scholar
  35. 35.
    Üstebay D, Oreshkin B, Coates M, Rabbat M (2008) Rates of convergence for greedy gossip with eavesdropping. In: Proceedings of the Allerton Conference on Communication, Control, and Computing. Monticello, pp 367–374Google Scholar
  36. 36.
    Üstebay D, Rabbat M Efficiently reaching consensus on the largest entries of a vector. In: IEEE Conference on Decision and Control (CDC) ’12, Maui, HI, USAGoogle Scholar
  37. 37.
    Xiao L, Boyd S (2004) Fast linear iterations for distributed averaging. Syst Control Lett 53(1):65–78MathSciNetCrossRefMATHGoogle Scholar
  38. 38.
    Zhao F, Shin J, Reich J (2002) Information-driven dynamic sensor collaboration. IEEE Signal Process Mag 19(2):61–72Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Deniz Üstebay
    • 1
  • Rui Castro
    • 2
  • Mark Coates
    • 1
  • Michael Rabbat
    • 1
  1. 1.Department of Electrical and Computer EngineeringMcGill UniversityMontrealCanada
  2. 2.Department of MathematicsEindhoven University of TechnologyEindhovenThe Netherlands

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