论文标题
非线性过滤的二元性I：可观察性
Duality for Nonlinear Filtering I: Observability
论文作者
论文摘要
本文涉及对二元理论的发展和使用，用于隐藏的马尔可夫模型（HMM），并具有白噪声观察。这项工作的主要贡献是将向后的随机微分方程（BSDE）作为双控制系统。一个关键结果是，HMM的随机可观察性（分别可检测性）用双重术语表示：双重控制系统的可控性（分别稳定性）。讨论了可控性的所有方面，即，讨论了可控空间和可控性的定义，以及它们的属性和明确的公式。提出的二元性被证明是线性系统理论中经典二元性的确切扩展。然后，可以关联并比较线性和非线性系统。这种关系的并排摘要以表格形式给出（表〜II）。
This paper is concerned with the development and use of duality theory for a hidden Markov model (HMM) with white noise observations. The main contribution of this work is to introduce a backward stochastic differential equation (BSDE) as a dual control system. A key outcome is that stochastic observability (resp. detectability) of the HMM is expressed in dual terms: as controllability (resp. stabilizability) of the dual control system. All aspects of controllability, namely, definition of controllable space and controllability gramian, along with their properties and explicit formulae, are discussed. The proposed duality is shown to be an exact extension of the classical duality in linear systems theory. One can then relate and compare the linear and the nonlinear systems. A side-by-side summary of this relationship is given in a tabular form (Table~II).
