5 research outputs found
On the Mathematical Theory of Ensemble (Linear-Gaussian) Kalman-Bucy Filtering
The purpose of this review is to present a comprehensive overview of the
theory of ensemble Kalman-Bucy filtering for linear-Gaussian signal models. We
present a system of equations that describe the flow of individual particles
and the flow of the sample covariance and the sample mean in continuous-time
ensemble filtering. We consider these equations and their characteristics in a
number of popular ensemble Kalman filtering variants. Given these equations, we
study their asymptotic convergence to the optimal Bayesian filter. We also
study in detail some non-asymptotic time-uniform fluctuation, stability, and
contraction results on the sample covariance and sample mean (or sample error
track). We focus on testable signal/observation model conditions, and we
accommodate fully unstable (latent) signal models. We discuss the relevance and
importance of these results in characterising the filter's behaviour, e.g. it's
signal tracking performance, and we contrast these results with those in
classical studies of stability in Kalman-Bucy filtering. We provide intuition
for how these results extend to nonlinear signal models and comment on their
consequence on some typical filter behaviours seen in practice, e.g.
catastrophic divergence