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.
This m-file simulates MPSK (BPSK,QPSK,8PSK)with theoretical and simulated results using Gray coding. Numerical examples of a satellite link design are shown using QPSK and/or 8PSK when the bit rate(Rb)is greater than the channel bandwidth Wc (Band-limited channel).
