Convergence Analysis of a Family of Robust Kalman Filters Based on the Contraction Principle

DOI10.1137/16M1099078zbMath1374.60074arXiv1705.05286OpenAlexW2614212589MaRDI QIDQ5370982

Mattia Zorzi

Publication date: 24 October 2017

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

Full work available at URL: https://arxiv.org/abs/1705.05286

zbMATH Keywords

Kalman filterRiccati equationcontraction mappingThompson's part metricblock updaterisk-sensitive filtering

Mathematics Subject Classification ID

Filtering in stochastic control theory (93E11) Sensitivity (robustness) (93B35) Signal detection and filtering (aspects of stochastic processes) (60G35)

Related Items (8)

Reduction of discrete algebraic Riccati equations: elimination of generalized eigenvalues on the unit circle ⋮ Some iterative methods for the largest positive definite solution to a class of nonlinear matrix equation ⋮ Asymptotic properties of linear filter for deterministic processes ⋮ Robust fixed-lag smoothing under model perturbations ⋮ Robust distributed Kalman filtering with event-triggered communication ⋮ Contraction analysis for fractional-order nonlinear systems ⋮ The geometry of the generalized algebraic Riccati equation and of the singular Hamiltonian system ⋮ On the reduction of the continuous-time generalized algebraic Riccati equation: an effective procedure for solving the singular LQ problem with smooth solutions

Cites Work

• Unnamed Item
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• The generalized continuous algebraic Riccati equation and impulse-free continuous-time LQ optimal control
• The symplectic semigroup and Riccati differential equations
• An interpretation of the dual problem of the THREE-like approaches
• On the exponential metric increasing property.
• On the robustness of the Bayes and Wiener estimators under model uncertainty
• The generalised discrete algebraic Riccati equation in linear-quadratic optimal control
• Rational approximations of spectral densities based on the Alpha divergence
• The contraction rate in Thompson's part metric of order-preserving flows on a cone -- application to generalized Riccati equations
• Hermitian solutions of the equation \(X=Q+NX^{-1}N^*\)
• A Contraction Analysis of the Convergence of Risk-Sensitive Filters
• Multivariate Spectral Estimation Based on the Concept of Optimal Prediction
• A New Family of High-Resolution Multivariate Spectral Estimators
• Kalman Filtering with Random Coefficients and Contractions
• A Birkhoff Contraction Formula with Applications to Riccati Equations
• Robust Least-Squares Estimation With a Relative Entropy Constraint
• Linear estimation in Krein spaces. I. Theory
• Linear estimation in Krein spaces. II. Applications
• Robustness and risk-sensitive filtering
• Robust Kalman Filtering Under Model Perturbations
• Robust State Space Filtering Under Incremental Model Perturbations Subject to a Relative Entropy Tolerance
• Robustness
• Invariant metrics, contractions and nonlinear matrix equations
• On Certain Contraction Mappings in a Partially Ordered Vector Space

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