Proximal Approximate Inference in 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 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.