Perturbations and projections of Kalman-Bucy semigroups

Abstract

We analyse various perturbations and projections of Kalman-Bucy semigroups and Riccati equations. For example, covariance inflation-type perturbations and localisation methods (projections) are common in the ensemble Kalman filtering literature. In the limit of these ensemble methods, the regularised sample covariance tends toward a solution of a perturbed/projected Riccati equation. With this motivation, results are given characterising the error between the nominal and regularised Riccati flows and Kalman-Bucy filtering distributions. New projection-type models are also discussed; e.g. Bose-Mesner projections. These regularisation models are also of interest on their own, and in, e.g., differential games, control of stochastic/jump processes, and robust control.

References in corpus (7)

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• Wishart distributions for decomposable covariance graph models
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Cited by in corpus (8)

• McKean-Vlasov SDEs in nonlinear filtering
• A perturbation analysis of stochastic matrix Riccati diffusions
• On the stability of matrix-valued Riccati diffusions
• On the Mathematical Theory of Ensemble (Linear-Gaussian) Kalman-Bucy Filtering
• Performance analysis of local ensemble Kalman filter
• On One-Dimensional Riccati Diffusions
• Stability Properties of Systems of Linear Stochastic Differential Equations with Random Coefficients
• Analysis of the feedback particle filter with diffusion map based approximation of the gain