Particle-kernel estimation of the filter density in state-space models

Understand

Sequential Monte Carlo (SMC) methods, also known as particle filters, are simulation-based recursive algorithms for the approximation of the a posteriori probability measures generated by state-space dynamical models.

• At any given time $t$, a SMC method produces a set of samples over the state space of the system of interest (often termed "particles") that is used to build a discrete and random approximation of the posterior probability distribution of the state variables, conditional on a sequence of available observations.
• One potential application of the methodology is the estimation of the densities associated to the sequence of a posteriori distributions.
• While practitioners have rather freely applied such density approximations in the past, the issue has received less attention from a theoretical perspective.