Marginalized Particle Filtering and Related Filtering Techniques as   Message Passing
  In this manuscript a factor graph approach is employed to investigate the recursive filtering problem for a mixed linear/nonlinear state-space model, i.e. for a model whose state vector can be partitioned in a linear state variable (characterized by conditionally linear dynamics) and a non linear state variable. Our approach allows us to show that: a) the factor graph characterizing the considered filtering problem is not cycle free; b) in the case of conditionally linear Gaussian systems, applying the sum-product rule, together with different scheduling procedures for message passing, to this graph results in both known and novel filtering techniques. In particular, it is proved that, on the one hand, adopting a specific message scheduling for forward only message passing leads to marginalized particle filtering in a natural fashion; on the other hand, if iterative strategies for message passing are employed, novel filtering methods, dubbed turbo filters for their conceptual resemblance to the turbo decoding methods devised for concatenated channel codes, can be developed. 
Giorgio M. Vitetta, Emilio Sirignano, Francesco Montorsi and Matteo   Sola
math.ST cs.SY stat.TH