Nonlinear filtering of smooth signals

被引：2

作者：

Khasminskii, R ^{[1
]}

机构：

[1] Wayne State Univ, Dept Math, Detroit, MI 48202 USA

来源：

STOCHASTICS AND DYNAMICS | 2005年 / 5卷 / 01期

基金：

美国国家科学基金会;

关键词：

nonlinear estimation; Kalman filter; Lyapunov function; stochastic differential equation; on-line estimation;

D O I：

10.1142/S0219493705001262

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

A nonlinear online Kalman type filter is proposed for the estimation of unknown function S(t) with the known smoothness)3 for, the diffusion observed process with, small, of the order epsilon(2), diffusion coefficient. Assuming that the drift coefficient of the observed process depends on an unknown function S(t), we propose an approach to the analysis of this estimator based on the Lyapunov's functions method. The best possible rate of convergence of risks to 0, as epsilon -> 0, is proven for beta <= 2.

引用

页码：27 / 35

页数：9

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