We present a particle filter construction for a system that exhibits

time-scale separation. The separation of time-scales allows two simplifications

that we exploit: i) The use of the averaging principle for the

dimensional reduction of the system needed to solve for each particle

and ii) the factorization of the transition probability which allows the

Rao-Blackwellization of the filtering step. Both simplifications can be

implemented using the coarse projective integration framework. The

resulting particle filter is faster and has smaller variance than the particle

filter based on the original system. The convergence of the new

particle filter to the analytical filter for the original system is proved

and some numerical results are provided.