  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.
