  Marginalization techniques are presented for the Bayesian filtering problem
under the assumption of Gaussian priors and posteriors and a set of
sequentially more constraining state space model assumptions. The techniques
provide the capabilities to 1) reduce the filtering problem to essential
marginal moment integrals, 2) combine model and numerical approximations to the
moment integrals, and 3) decouple modelling and system composition. Closed-form
expressions of the posterior means and covariances are developed as functions
of subspace projection matrices, subsystem models, and the marginal moment
integrals. Finally, we review prior work and how the results relate to Kalman
and marginalized particle filtering techniques.
