Finite Dimensional Estimation Algebras with State Dimension 3 and rank 2, I: Linear Structure of Wong Matrix

DOI10.1137/16M1065471zbMath1430.17042OpenAlexW2776902850MaRDI QIDQ4599727

Ji Shi, Stephen Shing-Toung Yau

Publication date: 4 January 2018

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

Full work available at URL: https://doi.org/10.1137/16m1065471

zbMATH Keywords

estimation algebranonlinear driftfinite dimensional filternonmaximal rank

Mathematics Subject Classification ID

Filtering in stochastic control theory (93E11) Signal detection and filtering (aspects of stochastic processes) (60G35) Initial value problems for second-order parabolic equations (35K15) Solvable, nilpotent (super)algebras (17B30)

Related Items (7)

General convergence result for continuous-discrete feedback particle filter ⋮ 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 ⋮ Finite dimensional estimation algebras with state dimension 3 and rank 2, Mitter conjecture ⋮ New Classes of Finite Dimensional Filters with Nonmaximal Rank Estimation Algebra on State Dimension $n$ and Linear Rank $n-2$ ⋮ The novel classes of finite dimensional filters with non-maximal rank estimation algebra on state dimension four and rank of one

Cites Work

• New classes of finite-dimensional nonlinear filters
• On a new class of finite dimensional estimation algebras
• Theorems on the structure of finite dimensional estimation algebras
• New explicit filters and smoothers for diffusions with nonlinear drift and measurements
• Structure theorem for five-dimensional estimation algebras
• Stochastic differential equations for the non linear filtering problem
• Mitter conjecture and structure theorem for six-dimensional estimation algebras
• 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
• Classification of Estimation Algebras with State Dimension 2
• On a Necessary and Sufficient Condition for Finite Dimensionality of Estimation Algebras
• Exact finite-dimensional filters for certain diffusions with nonlinear drift
• Finite-Dimensional Filters with Nonlinear Drift. II: Brockett’s Problem on Classification of Finite-Dimensional Estimation Algebras
• Complete classification of finite-dimensional estimation algebras of maximal rank
• Classification of four-dimensional estimation algebras
• Hermite Spectral Method to 1-D Forward Kolmogorov Equation and Its Application to Nonlinear Filtering Problems
• Complete Real Time Solution of the General Nonlinear Filtering Problem Without Memory
• Classification of finite-dimensional estimation algebras of maximal rank with arbitrary state–space dimension and mitter conjecture
• On Global Representations of the Solutions of Linear Differential Equations as a Product of Exponentials
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