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 mixed linear/nonlinear state-space models. 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, a novel filtering method, dubbed turbo filter for its 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 University of Modena and Reggio Emilia Department of Engineering ”Enzo Ferrari” Via P. Vivarelli 10/1, 41125 Modena Italy email: [email protected], [email protected], [email protected], [email protected]