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Marginalization techniques are presented for the Bayesian filtering problemunder the assumption of Gaussian priors and posteriors and a set ofsequentially more constraining state space model assumptions. The techniquesprovide the capabilities to 1) reduce the filtering problem to essentialmarginal moment integrals, 2) combine model and numerical approximations to themoment integrals, and 3) decouple modelling and system composition. Closed-formexpressions of the posterior means and covariances are developed as functionsof subspace projection matrices, subsystem models, and the marginal momentintegrals. Finally, we review prior work and how the results relate to Kalmanand marginalized particle filtering techniques.

Marginalized Bayesian filtering with Gaussian priors and posteriors