  The crucial step in designing a particle filter for a particular application
is the choice of importance density. The optimal scheme is to use the
conditional posterior density of the state, but this cannot be sampled or
calculated analytically in most case. In practice, approximations of this
density are used, particularly Gaussian densities based on linearisation or the
unscented transform. For many highly nonlinear or non-Gaussian models, these
approximations can be poor, leading to degeneracy of the particle approximation
or even the filter "losing track" completely. In this paper, we develop a new
mechanism for approximating the optimal importance density, which we call the
progressive proposal method. This works by introducing the observation
progressively and performing a series of state updates, each using a local
Gaussian approximation to the optimal importance density. A number of
refinements and extensions to the basic algorithm are also introduced.
Simulations are used to demonstrate an improvement in performance over simpler
particle filters on a number of applications.
