LARGE DEVIATION PRINCIPLE IN DISCRETE TIME NONLINEAR FILTERING

被引：0

作者：

Anugu, Sumith reddy ^{[1
]}

机构：

[1] Rice Univ, Dept Computat Appl Math & Operat Res, Houston, TX 77005 USA

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2024年 / 62卷 / 06期

关键词：

Laplace asymptotics; large deviation principle; nonlinear filtering; small observation and signal noise; minimum energy estimate;

D O I：

10.1137/23M1589979

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this work, we study the behavior of discrete time nonlinear filters when the signal and observations are small. It will be shown that if these noises are of the same order, then there is a nontrivial limiting behavior of the corresponding conditional distribution. In addition, we establish a large deviation principle for the conditional distribution. The proof is via the weak convergence approach. However, the main hurdle in the proof is the difficulty in uniquely characterizing the limiting conditional distribution, as we can only identify the support of the limiting conditional distribution. This uniquely identifies the limit only in the case when the support is a singleton set. Therefore, we construct an appropriately equivalent problem where the aforementioned support is a singleton set. After establishing the large deviation principle, we immediately infer the large deviation principle of the original problem from the equivalence.

引用

页码：3121 / 3144

页数：24

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