Recursive Entropic Variational Inference for Nonlinear State-Space Models

We present a class of algorithms for state estimation in nonlinear, non-Gaussian state-space models.

Our approach is based on a variational Lagrangian formulation that casts Bayesian inference as a sequence of entropic trust-region updates subject to dynamic consistency constraints.

This framework gives rise to a family of forward-backward algorithms whose structure is determined by the chosen factorization of the variational posterior.

By focusing on Gauss--Markov approximations, we derive recursive schemes with favorable computational complexity.

For general nonlinear, non-Gaussian models, we close the recursions using generalized statistical linear regression and Fourier--Hermite moment matching.