Posterior linearisation filter for non-linear state transformation noises

This paper is concerned with discrete time Kalman-type filtering with state transition and measurement noises that may be non-additive or non-linearly transformed. More specifically, we extend the iterative estimation algorithm Posterior Linearization Filter (PLF) for estimation with this kind of noises. The approach solves the prediction and update step simultaneously, which allows to use the PLF iterations to improve the estimation in the non-linear state transition model. The proposed algorithm also produces single step fixed-lag smoothing estimates. We show in examples how the proposed approach can be used with non-Gaussian state transition noises and non-linearly transformed state transition noises.