论文标题
线性设置会员过滤器相对于初始条件的稳定性：观察信息的透视
Stability of Linear Set-Membership Filters With Respect to Initial Conditions: An Observation-Information Perspective
论文作者
论文摘要
相对于（W.R.T.）的滤波器稳定性问题是指初始状态不正确的先前信息引起的不可靠的过滤过程。本文着重分析和解决稳定问题W.R.T.线性时间影响系统的经典设置会员过滤器（SMF）的初始条件，在文献中尚未对其进行充分了解。为此，我们提出了一个新概念 - 观察信息塔（OIT），该概念描述了测量值如何以设定的交流方式影响估计，而不依赖初始条件。提出的OIT可以实现严格的稳定性分析，新的SMFing框架以及有效的过滤算法。具体而言，基于OIT，明确的稳定性W.R.T.的必要条件和足够的条件。为经典的SMFing框架提供了初始条件。此外，OIT启发了一个稳定性保证的SMFing框架，该框架完全处理了稳定性问题W.R.T.初始条件。最后，通过OIT启发的框架，我们开发了一个快速稳定的约束界限SMF，这极大地克服了包装效果。
The issue of filter stability with respect to (w.r.t.) the initial condition refers to the unreliable filtering process caused by improper prior information of the initial state. This paper focuses on analyzing and resolving the stability issue w.r.t. the initial condition of the classical Set-Membership Filters (SMFs) for linear time-invariance systems, which has not yet been well understood in the literature. To this end, we propose a new concept -- the Observation-Information Tower (OIT), which describes how the measurements affect the estimate in a set-intersection manner without relying on the initial condition. The proposed OIT enables a rigorous stability analysis, a new SMFing framework, as well as an efficient filtering algorithm. Specifically, based on the OIT, explicit necessary and sufficient conditions for stability w.r.t. the initial condition are provided for the classical SMFing framework. Furthermore, the OIT inspires a stability-guaranteed SMFing framework, which fully handles the stability issue w.r.t. the initial condition. Finally, with the OIT-inspired framework, we develop a fast and stable constrained zonotopic SMF, which significantly overcomes the wrapping effect.
