Marginalized Bayesian filtering with Gaussian priors and posteriors

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.