  The particle filter is a popular Bayesian filtering algorithm for use in
cases where the state-space model is nonlinear and/or the random terms (initial
state or noises) are non-Gaussian distributed. We study the behavior of the
error in the particle filter algorithm as the number of particles gets large.
After a decomposition of the error into two terms, we show that the difference
between the estimator and the conditional mean is asymptotically normal when
the resampling is done at every step in the filtering process. Two
nonlinear/non-Gaussian examples are tested to verify this conclusion.
