Long-Time Asymptotics of the Filtering Distribution for Partially Observed Chaotic Dynamical Systems
Long-Time Asymptotics of the Filtering Distribution for Partially Observed Chaotic Dynamical Systems
复制标题
部分可观测混沌动力系统滤波分布的长时渐近
DOI：
10.1137/140997336
复制
发表时间：
2014
期刊：
影响因子：
--
通讯作者：
A. Stuart
中科院分区：
文献类型：
--
作者：
D. Sanz;A. Stuart
滤波分布是给定噪声观测的动态系统状态的时间演化概率分布。我们研究了离散时间，随机初始化的信号，根据一个确定性的地图$\Psi$演变的概率分布的大时间渐近性。假设观测值包括信号的低维投影，由算子P$给出，受加性噪声的影响。我们解决的问题，这些意见是否包含足够的信息，以准确地重建信号。在一个一般的框架中，我们建立了条件$\Psi$和$P$下，滤波分布集中在小噪声，长时间渐近制度的信号。线性系统，洛伦兹'63和'96模型，以及二维环面上的Navier-Stokes方程都在该理论的范围内。我们的主要研究结果来作为一个副产品的可计算的界限，独立的利益，次优过滤器的基础上新的变种…
The filtering distribution is a time-evolving probability distribution on the state of a dynamical system given noisy observations. We study the large-time asymptotics of this probability distribution for discrete-time, randomly initialized signals that evolve according to a deterministic map $\Psi$. The observations are assumed to comprise a low-dimensional projection of the signal, given by an operator $P$, subject to additive noise. We address the question of whether these observations contain sufficient information to accurately reconstruct the signal. In a general framework, we establish conditions on $\Psi$ and $P$ under which the filtering distributions concentrate around the signal in the small-noise, long-time asymptotic regime. Linear systems, the Lorenz '63 and '96 models, and the Navier--Stokes equation on a two-dimensional torus are within the scope of the theory. Our main findings come as a by-product of computable bounds, of independent interest, for suboptimal filters based on new variants...
影响因子：
1.8
作者：
Beskos, Alexandros;Crisan, Dan;Jasra, Ajay
通讯作者：
Jasra, Ajay