This letter is concerned with solving continuous-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 are presented in order to illustrate practical use of the method.

翻译：本信涉及通过使用泰勒时空扩张(TME)计划解决连续分解高斯平滑问题。在拟议的平滑方法中,我们采用TME方法来估计动态模型中随机差分方程的过渡密度。此外,我们得出了TME平滑估算中(以平均平方意义)的理论错误,表明光滑在薄弱假设下是稳定的。提出了数字实验,以说明该方法的实际用途。