Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

Error analysis for numerical formulation of particle filter

Pages: 1337 - 1354, Volume 20, Issue 5, July 2015      doi:10.3934/dcdsb.2015.20.1337

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Xiaoying Han - 221 Parker Hall, Department of Mathematics and Statistics, Auburn University, Auburn, AL 36849, United States (email)
Jinglai Li - Institute of Natural sciences, Department of Mathematics, MOE Key Lab of Scienti c and Engineering Computing, Shanghai JiaoTong University, 800 Dongchuan Rd, Minhang 200240, Shanghai, China (email)
Dongbin Xiu - Department of Mathematics, Scientific Computing and Imagining Institute, The University of Utah, Salt Lake City, UT 84112, United States (email)

Abstract: As an approximation of the optimal stochastic filter, particle filter is a widely used tool for numerical prediction of complex systems when observation data are available. In this paper, we conduct an error analysis from a numerical analysis perspective. That is, we investigate the numerical error, which is defined as the difference between the numerical implementation of particle filter and its continuous counterpart, and demonstrate that the error consists of discretization errors for solving the dynamic equations numerically and sampling errors for generating the random particles. We then establish convergence of the numerical particle filter to the continuous optimal filter and provide bounds for the convergence rate. Remarkably, our analysis suggests that more frequent data assimilation may lead to larger numerical errors of the particle filter. Numerical examples are provided to verify the theoretical findings.

Keywords:  Bayesian filer, data assimilation, particle filter, sequential Monte Carlo.
Mathematics Subject Classification:  Primary: 65C35; Secondary: 65C05.

Received: December 2013;      Revised: January 2015;      Available Online: May 2015.