Perturbations and projections of Kalman–Bucy semigroups

Adrian N. Bishop, Pierre Del Moral and Sahani D. Pathiraja

Stochastic Processes and their Applications, 2018, vol. 128, issue 9, 2857-2904

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.

Keywords: Data assimilation; Ensemble Kalman filters; Inflation models; Kalman–Bucy semigroups; Localisation models; Riccati equations; Sample covariance regularisation (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:128:y:2018:i:9:p:2857-2904

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DOI: 10.1016/j.spa.2017.10.006

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