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Convergence Analysis for the SMC‐MeMBer and SMC‐CBMeMBer Filters

Author

Listed:
  • Feng Lian
  • Chen Li
  • Chongzhao Han
  • Hui Chen

Abstract

The convergence for the sequential Monte Carlo (SMC) implementations of the multitarget multi‐Bernoulli (MeMBer) filter and cardinality‐balanced MeMBer (CBMeMBer) filters is studied here. This paper proves that the SMC‐MeMBer and SMC‐CBMeMBer filters, respectively, converge to the true MeMBer and CBMeMBer filters in the mean‐square sense and the corresponding bounds for the mean‐square errors are given. The significance of this paper is in theory to present the convergence results of the SMC‐MeMBer and SMC‐CBMeMBer filters and the conditions under which the two filters satisfy mean‐square convergence.

Suggested Citation

  • Feng Lian & Chen Li & Chongzhao Han & Hui Chen, 2012. "Convergence Analysis for the SMC‐MeMBer and SMC‐CBMeMBer Filters," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:584140
    DOI: 10.1155/2012/584140
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    References listed on IDEAS

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    1. Gendai Gu & Shenghua Wang & Yeol Je Cho, 2011. "Strong Convergence Algorithms for Hierarchical Fixed Points Problems and Variational Inequalities," Journal of Applied Mathematics, Hindawi, vol. 2011, pages 1-17, September.
    2. Vittorio Colao, 2012. "On the Convergence of Iterative Processes for Generalized Strongly Asymptotically ϕ‐Pseudocontractive Mappings in Banach Spaces," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    3. Gendai Gu & Shenghua Wang & Yeol Je Cho, 2011. "Strong Convergence Algorithms for Hierarchical Fixed Points Problems and Variational Inequalities," Journal of Applied Mathematics, John Wiley & Sons, vol. 2011(1).
    4. Vittorio Colao, 2012. "On the Convergence of Iterative Processes for Generalized Strongly Asymptotically 𠜙 -Pseudocontractive Mappings in Banach Spaces," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-18, November.
    5. Prasit Cholamjiak & Suthep Suantai & Yeol Je Cho, 2012. "Strong Convergence to Solutions of Generalized Mixed Equilibrium Problems with Applications," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-18, January.
    6. Prasit Cholamjiak & Suthep Suantai & Yeol Je Cho, 2012. "Strong Convergence to Solutions of Generalized Mixed Equilibrium Problems with Applications," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
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