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In this manuscript a factor graph approach is employed to investigate therecursive filtering problem for a mixed linear/nonlinear state-space model,i.e. for a model whose state vector can be partitioned in a linear statevariable (characterized by conditionally linear dynamics) and a non linearstate variable. Our approach allows us to show that: a) the factor graphcharacterizing the considered filtering problem is not cycle free; b) in thecase of conditionally linear Gaussian systems, applying the sum-product rule,together with different scheduling procedures for message passing, to thisgraph results in both known and novel filtering techniques. In particular, itis proved that, on the one hand, adopting a specific message scheduling forforward only message passing leads to marginalized particle filtering in anatural fashion; on the other hand, if iterative strategies for message passingare employed, novel filtering methods, dubbed turbo filters for theirconceptual resemblance to the turbo decoding methods devised for concatenatedchannel codes, can be developed.

Marginalized Particle Filtering and Related Filtering Techniques as Message Passing