Asymptotic Stability of the Optimal Filter with Respect toIts Initial Condition
Asymptotic Stability of the Optimal Filter with Respect toIts Initial Condition
复制标题
最优滤波器相对于初始条件的渐近稳定性
DOI：
10.1137/s0363012993256617
复制
发表时间：
1996
影响因子：
2.2
通讯作者：
É. Pardoux
中科院分区：
文献类型：
--
作者：
D. Ocone;É. Pardoux
考虑在加性白色噪声中观察到的扩散信号的估计问题。如果用不正确的先验分布初始化的滤波方程的解在时间上渐近地接近真实的条件分布，则滤波器被称为相对于初始条件的扰动是渐近稳定的。本文给出了线性滤波问题和具有极限遍历行为的信号的渐近稳定性结果。对于线性情况，卡尔曼滤波的Riccati方程的稳定性被用来导出线性滤波器对于可能的非高斯初始条件的几乎必然渐近稳定性。在非线性的情况下，渐近稳定性弱收敛意义下的信号扩散的法律收敛到一个不变的分布的过滤器。
Consider the problem of estimation of a diffusion signal observed in additive white noise. If the solution to the filtering equations, initialized with an incorrect prior distribution, approaches the true conditional distribution asymptotically in time, then the filter is said to be asymptotically stable with respect to perturbations of the initial condition. This paper presents asymptotic stability results for linear filtering problems and for signals with limiting ergodic behavior. For the linear case, stability of the Riccati equation of Kalman filtering is used to derive almost sure asymptotic stability of linear filters for possibly non-Gaussian initial conditions. In the nonlinear case, asymptotic stability in a weak convergence sense is shown for filters of signal diffusions which converge in law to an invariant distribution.