a stable particle filter in high

In high dimensionas, standard particle filters can have a cost that is exponential in (d) for the algorithm to be stable in an appropriate sense. This paper proposed a new particle filter, called space-time particle filter, for a specific family of state space models in discrete time.

The authors break the (k)-th time step of the particle filter into (tau_{k,d}) space-steps and run a system of (N) independent particle filters for these steps.

The Space-Time Particle Filter

The authors develop an algorithm that combines a local filter running (d) space-step using (M_d) particles, with a global filter making time-steps and uses (N) particles.