# American Institute of Mathematical Sciences

July  2015, 20(5): 1337-1354. doi: 10.3934/dcdsb.2015.20.1337

## Error analysis for numerical formulation of particle filter

 1 221 Parker Hall, Department of Mathematics and Statistics, Auburn University, Auburn, AL 36849 2 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 3 Department of Mathematics, Scientific Computing and Imagining Institute, The University of Utah, Salt Lake City, UT 84112, United States

Received  December 2013 Revised  January 2015 Published  May 2015

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.
Citation: Xiaoying Han, Jinglai Li, Dongbin Xiu. Error analysis for numerical formulation of particle filter. Discrete & Continuous Dynamical Systems - B, 2015, 20 (5) : 1337-1354. doi: 10.3934/dcdsb.2015.20.1337
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