Iterated extended Kalman smoothing with expectation-propagation

We formulate extended Kalman smoothing in an expectation-propagation (EP) framework. The approximation involved (a local linearization) can be looked upon as a ´collapse´ of a non-Gaussian belief state onto a Gaussian form. This formulation allows us to come up with better approximations to the belief states, since we can iterate the algorithm until no further refinement of the beliefs is obtained. Compared to the standard extended Kalman smoother, we linearize around the mode of the actual two-slice belief state instead of the predicted mean of the one-slice belief. In initial experiments with a one-dimensional nonlinear dynamical system we found that our method improves over the extended Kalman filter and performs comparable to the unscented Kalman filter, whereas only second-order approximations are being made. The EP-formulation in principle allows for incorporation of higher-order approximations, possibly leading to further improvements.