  The term ``sequential Monte Carlo methods'' or, equivalently, ``particle
filters,'' refers to a general class of iterative algorithms that performs
Monte Carlo approximations of a given sequence of distributions of interest
(\pi_t). We establish in this paper a central limit theorem for the Monte Carlo
estimates produced by these computational methods. This result holds under
minimal assumptions on the distributions \pi_t, and applies in a general
framework which encompasses most of the sequential Monte Carlo methods that
have been considered in the literature, including the resample-move algorithm
of Gilks and Berzuini [J. R. Stat. Soc. Ser. B Stat. Methodol. 63 (2001)
127-146] and the residual resampling scheme. The corresponding asymptotic
variances provide a convenient measurement of the precision of a given particle
filter. We study, in particular, in some typical examples of Bayesian
applications, whether and at which rate these asymptotic variances diverge in
time, in order to assess the long term reliability of the considered algorithm.
