  Many real-world problems require one to estimate parameters of interest, in a
Bayesian framework, from data that are collected sequentially in time.
Conventional methods for sampling from posterior distributions, such as {Markov
Chain Monte Carlo} can not efficiently address such problems as they do not
take advantage of the data's sequential structure. To this end, sequential
methods which seek to update the posterior distribution whenever a new
collection of data become available are often used to solve these types of
problems. Two popular choices of sequential method are the Ensemble Kalman
filter (EnKF) and the sequential Monte Carlo sampler (SMCS). An advantage of
the SMCS method is that, unlike the EnKF method that only computes a Gaussian
approximation of the posterior distribution, SMCS can draw samples directly
from the posterior. Its performance, however, depends critically upon the
kernels that are used. In this work, we present a method that constructs the
kernels of SMCS using an EnKF formulation, and we demonstrate the performance
of the method with numerical examples.
