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Generalised particle filters with Gaussian mixtures

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  • Crisan, D.
  • Li, K.

Abstract

Stochastic filtering is defined as the estimation of a partially observed dynamical system. Approximating the solution of the filtering problem with Gaussian mixtures has been a very popular method since the 1970s. Despite nearly fifty years of development, the existing work is based on the success of the numerical implementation and is not theoretically justified. This paper fills this gap and contains a rigorous analysis of a new Gaussian mixture approximation to the solution of the filtering problem. We deduce the L2-convergence rate for the approximating system and show some numerical examples to test the new algorithm.

Suggested Citation

  • Crisan, D. & Li, K., 2015. "Generalised particle filters with Gaussian mixtures," Stochastic Processes and their Applications, Elsevier, vol. 125(7), pages 2643-2673.
    • Handle: RePEc:eee:spapps:v:125:y:2015:i:7:p:2643-2673
    DOI: 10.1016/j.spa.2015.01.008
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    References listed on IDEAS

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    1. Christophe Andrieu & Arnaud Doucet, 2002. "Particle filtering for partially observed Gaussian state space models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 827-836, October.
    2. Ren, Yao-Feng & Liang, Han-Ying, 2001. "On the best constant in Marcinkiewicz-Zygmund inequality," Statistics & Probability Letters, Elsevier, vol. 53(3), pages 227-233, June.
    3. Crisan, D. & Obanubi, O., 2012. "Particle filters with random resampling times," Stochastic Processes and their Applications, Elsevier, vol. 122(4), pages 1332-1368.
    4. Rong Chen & Jun S. Liu, 2000. "Mixture Kalman filters," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(3), pages 493-508.
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