论文标题
连续的散差过滤和平滑欧几里得空间的平滑
Continuous-Discrete Filtering and Smoothing on Submanifolds of Euclidean Space
论文作者
论文摘要
在本文中，当状态变量在欧几里得空间的某些子序列中演变时，研究了连续离散时间过滤和平滑的问题，这可能没有通常的lebesgue度量。提出了针对预测和平滑问题的形式表达，这与经典结果一致，除了发电机的形式伴随一般是不同的。对于近似滤波和平滑，采用投影方法，事实证明，预测和平滑方程与状态变量在欧几里得空间中演变时相同。该方法用于根据Von Mises-Fisher分布来开发投影过滤器和Smoothers。
In this paper the issue of filtering and smoothing in continuous discrete time is studied when the state variable evolves in some submanifold of Euclidean space, which may not have the usual Lebesgue measure. Formal expressions for prediction and smoothing problems are derived, which agree with the classical results except that the formal adjoint of the generator is different in general. For approximate filtering and smoothing the projection approach is taken, where it turns out that the prediction and smoothing equations are the same as in the case when the state variable evolves in Euclidean space. The approach is used to develop projection filters and smoothers based on the von Mises-Fisher distribution.
