论文标题
泰勒矩膨胀，用于连续污染的高斯滤波和平滑
Taylor Moment Expansion for Continuous-Discrete Gaussian Filtering and Smoothing
论文作者
论文摘要
该论文与连续二散状态空间模型中的非线性高斯滤波和平滑有关，在该模型中，动态模型的配方为ITôStochastic微分方程（SDE），并且在离散时间瞬间获得了测量。我们提出了新型的泰勒矩膨胀（TME）高斯滤波器，并更光滑，该滤波器近似于SDE的力矩，并具有暂时的泰勒膨胀。与经典的线性化或ITô-泰勒方法不同，泰勒的扩展是直接和时间变量的矩函数形成的，而不是通过对模型中的非线性函数使用泰勒扩展。我们分析了理论特性，包括TME高斯滤波器的协方差估计和稳定性的积极确定性以及更光滑的。通过数值实验，我们证明了所提出的TME高斯滤波器，并且在估计精度和数值稳定性方面显着优于最新方法。
The paper is concerned with non-linear Gaussian filtering and smoothing in continuous-discrete state-space models, where the dynamic model is formulated as an Itô stochastic differential equation (SDE), and the measurements are obtained at discrete time instants. We propose novel Taylor moment expansion (TME) Gaussian filter and smoother which approximate the moments of the SDE with a temporal Taylor expansion. Differently from classical linearisation or Itô--Taylor approaches, the Taylor expansion is formed for the moment functions directly and in time variable, not by using a Taylor expansion on the non-linear functions in the model. We analyse the theoretical properties, including the positive definiteness of the covariance estimate and stability of the TME Gaussian filter and smoother. By numerical experiments, we demonstrate that the proposed TME Gaussian filter and smoother significantly outperform the state-of-the-art methods in terms of estimation accuracy and numerical stability.
