Complete Classification of Finite Dimensional Estimation Algebras With State Dimension n, Linear Rank n-1, and Constant Wong Matrix

• 成果类型: Article
• 署名作者: Yu, Hongyu; Jiao, Xiaopei; Yau, Stephen S. -T.
• 署名单位: Tsinghua University; Yanqi Lake Beijing Institute of Mathematical Sciences & Applications
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3266012
• 发表日期: 2024
• 页码: 295-302
• 关键词: estimation; Algebra; Filtering theory; matrices; Aircraft navigation; TIN; Orbits; CLASSIFICATION; finite dimensional estimation algebras; nonmaximal rank; nonlinear filters; Wong matrix

摘要

Ever since the Lie algebra method was introduced to construct finite dimensional nonlinear filters by Brockett and Mitter independently, there has been an intense interest in classifying all finite dimensional estimation algebras and finding new classes of finite dimensional recursive filters. The estimation algebra method has been proven to be an invaluable tool in the nonlinear filtering theory. This article considers the finite dimensional estimation algebras derived from a nonlinear filtering system with state dimension n, linear rank n-1, and constant Wong matrix. Related theories of the underdetermined partial differential equations and the Euler operator are applied to classify the estimation algebras. It is proved that the Mitter conjecture holds and the dimension of the finite dimensional estimation algebras must be 2n or 2n+1 with the abovementioned conditions. Therefore, we can construct the explicit solution of filtering systems by Wei-Norman approach. This result is of great significance because it is the first classification of nonmaximal rank finite dimensional estimation algebras with arbitrary state dimension.