On the Bias of the SIR Filter in Parameter Estimation of the Dynamics Process of State Space Models

  • Tiancheng LiEmail author
  • Sara Rodríguez
  • Javier Bajo
  • Juan M. Corchado
  • Shudong Sun
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 373)


As a popular nonlinear estimation tool, the sampling importance resampling (SIR) filter has been applied with the expectation–maximization (EM) principle, including the typical maximum a posteriori (MAP) estimation and maximum likelihood (ML) estimation, for estimating the parameters of the state space model (SSM). This paper concentrates on an inevitable bias existing in the EM-SIR filter for estimating the dynamics process of the SSM. It is analyzed that the root reason for the bias is the sample impoverishment caused by the resampling procedure employed in the filter. A process noise simulated for the particle propagation that is larger than the real noise involved with the true state will be helpful to counteract sample impoverishment, thereby providing better filtering result. Correspondingly, the EM-SIR filter tends to yield a biased (larger-than-the-truth) estimate of the process noise if it is unknown and needs to be estimated. The bias is elaborated via a straightforward roughening approach by means of both qualitative logical deduction and quantitative numerical simulation. However, it seems hard to fully remove this bias in practice.


Particle filter expectation-maximization parameter estimation 


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Tiancheng Li
    • 1
    • 2
    Email author
  • Sara Rodríguez
    • 1
  • Javier Bajo
    • 3
  • Juan M. Corchado
    • 1
  • Shudong Sun
    • 2
  1. 1.BISITE group, Faculty of ScienceUniversity of SalamancaSalamancaSpain
  2. 2.School of Mechanical EngineeringNorthwestern Polytechnical UniversityFremontChina
  3. 3.Department of Artificial IntelligenceTechnical University of MadridMadridSpain

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