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-invariant 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.

中文翻译：

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线性集合成员过滤器相对于初始条件的稳定性：观测信息视角


相对于 （w.r.t.） 初始条件的滤波器稳定性问题是指由于初始状态的先验信息不正确而导致的不可靠的过滤过程。本文重点分析和解决线性时不变系统的经典集合成员滤波器 （SMF） 的初始条件的稳定性问题，该问题在文献中尚未得到很好的理解。为此，我们提出了一个新概念——观测信息塔 （OIT），它描述了测量如何以集合交集的方式影响估计，而不依赖于初始条件。提出的 OIT 支持严格的稳定性分析、新的 SMFing 框架以及高效的过滤算法。具体来说，在 OIT 的基础上，为经典的 SMFing 框架提供了明确的稳定性的必要和充分条件。此外，OIT 激发了一个稳定性保证的 SMFing 框架，该框架完全处理了初始条件的稳定性问题。最后，借助受 OIT 启发的框架，我们开发了一种快速稳定的约束生虫 SMF，它显着克服了包装效应。