  Sequential Monte Carlo techniques are useful for state estimation in
non-linear, non-Gaussian dynamic models. These methods allow us to approximate
the joint posterior distribution using sequential importance sampling. In this
framework, the dimension of the target distribution grows with each time step,
thus it is necessary to introduce some resampling steps to ensure that the
estimates provided by the algorithm have a reasonable variance. In many
applications, we are only interested in the marginal filtering distribution
which is defined on a space of fixed dimension. We present a Sequential Monte
Carlo algorithm called the Marginal Particle Filter which operates directly on
the marginal distribution, hence avoiding having to perform importance sampling
on a space of growing dimension. Using this idea, we also derive an improved
version of the auxiliary particle filter. We show theoretic and empirical
results which demonstrate a reduction in variance over conventional particle
filtering, and present techniques for reducing the cost of the marginal
particle filter with N particles from O(N2) to O(N logN).
