Finite-Dimensional Filters with Nonlinear Drift. II: Brockett’s Problem on Classification of Finite-Dimensional Estimation Algebras

DOI10.1137/S0363012991201660zbMath0809.93060OpenAlexW2036922159MaRDI QIDQ4286630

Wen-Lin Chiou, Stephen Shing-Toung Yau

Publication date: 26 April 1994

Published in: SIAM Journal on Control and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/s0363012991201660

zbMATH Keywords

nonlinear filters classification of estimation algebras

Mathematics Subject Classification ID

Filtering in stochastic control theory (93E11) Lie algebras of vector fields and related (super) algebras (17B66) Signal detection and filtering (aspects of stochastic processes) (60G35) Second-order elliptic equations (35J15) Solvable, nilpotent (super)algebras (17B30)

Related Items (19)

A note on estimation algebras on nonlinear filtering theory ⋮ Finite-dimensional filters with nonlinear drift. VI: Linear structure of $\Omega$ ⋮ Characterization of a subclass of finite-dimensional estimation algebras with maximal rank. Application to filtering ⋮ Explicit solution of a Kolmogorov equation ⋮ Direct method for Yau filtering system with nonlinear observations ⋮ 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* ⋮ Finite Dimensional Estimation Algebras with State Dimension 3 and rank 2, I: Linear Structure of Wong Matrix ⋮ 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 ⋮ Explicit Wei-Norman formulae for matrix Lie groups via Putzer's method ⋮ Structure theorem for five-dimensional estimation algebras ⋮ Finite dimensional filters with nonlinear drift. XI: Explicit solution of the generalized Kolmogorov equation in Brockett-Mitter program ⋮ Mitter conjecture and structure theorem for six-dimensional estimation algebras

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