Finite-dimensional filters with nonlinear drift. VI: Linear structure of \(\Omega\)

DOI10.1007/BF01211857zbMath0876.93090OpenAlexW1965581829MaRDI QIDQ1356631

Jie Chen, Stephen Shing-Toung Yau

Publication date: 3 December 1997

Published in: MCSS. Mathematics of Control, Signals, and Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01211857

zbMATH Keywords

estimation algebrafinite-dimensional nonlinear filter

Mathematics Subject Classification ID

Filtering in stochastic control theory (93E11) Signal detection and filtering (aspects of stochastic processes) (60G35)

Related Items (11)

Finite dimensional filters with non-linear drift IX Construction of finite dimensional estimation algebras of non-maximal rank ⋮ Log-Concave Posterior Densities Arising in Continuous Filtering and a Maximum A Posteriori Algorithm ⋮ Structure of finite dimensional exact estimation algebra on state dimension 3 and linear rank 2* ⋮ Hessian matrix non-decomposition theorem and its application to nonlinear filtering ⋮ Mitter conjecture for low dimensional estimation algebras in non-linear filtering† ⋮ New Classes of Finite Dimensional Filters with Nonmaximal Rank Estimation Algebra on State Dimension $n$ and Linear Rank $n-2$ ⋮ Classification of finite-dimensional estimation algebras of maximal rank with arbitrary state–space dimension and mitter conjecture ⋮ The novel classes of finite dimensional filters with non-maximal rank estimation algebra on state dimension four and rank of one ⋮ Complete classification of finite-dimensional estimation algebras of maximal rank ⋮ Structure theorem for five-dimensional estimation algebras ⋮ Mitter conjecture and structure theorem for six-dimensional estimation algebras

Cites Work

• Nonexistence of finite-dimensional filters for conditional statistics of the cubic sensor problem
• On a new class of finite dimensional estimation algebras
• Stochastic differential equations for the non linear filtering problem
• Des resultats de non existence de filtre de dimension finie
• Algebraic and Geometric Methods in Nonlinear Filtering
• Structure and Classification Theorems of Finite-Dimensional Exact Estimation Algebras
• On a Necessary and Sufficient Condition for Finite Dimensionality of Estimation Algebras
• A conditionally almost linear filtering problem with non-gaussian initial condition^∗
• On a multiplicative functional transformation arising in nonlinear filtering theory
• Finite-Dimensional Filters with Nonlinear Drift. II: Brockett’s Problem on Classification of Finite-Dimensional Estimation Algebras
• Finite-Dimensional Filters with Nonlinear Drift IV: Classification of Finite-Dimensional Estimation Algebras of Maximal Rank with State–Space Dimension 3
• Filtering formulae for partially observed linear systems with non-gaussian initial conditions
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