In this manuscript the application of a factor graph approach to the filtering problem for a mixed linear/nonlinear state-space model is investigated. In particular, after developing a factor graph for the considered model, a novel approximate recursive technique for solving such a problem is derived applying the sum-product algorithm and a specific scheduling procedure for message passing to this graph. Then, the application of this technique, dubbed turbo filtering for its conceptual resemblance with turbo decoding of concatenated channel codes, to linear Gaussian systems is investigated. Numerical results for specific state-space models show that turbo filtering can achieve a good performance-complexity tradeoff.