Non-linear Gaussian smoothing with Taylor moment expansion

This letter is concerned with solvingcontinuous-discrete Gaussian smoothing problems by using the Taylor moment expansion (TME) scheme. In the proposed smoothing method, we apply the TME method to approximate the transition density of the stochastic differential equation in the dynamic model. Furthermore, we derive a theoretical error bound (in the mean square sense) of the TME smoothing estimates showing that the smoother is stable under weak assumptions. Numerical experiments show that the proposed smoother outperforms a number of baseline smoothers.