Variational Bayesian Filtering

The use of the variational Bayes (VB) approximation in Bayesian filtering is studied, both as a means to accelerate marginalized particle filtering and as a deterministic local (one-step) approximation. The VB method of approximation is reviewed, together with restrictions that allow various computational savings to be achieved. These variants provide a range of algorithms that can be used in a principled tradeoff between quality of approximation and computational cost. In combination with marginalized particle filtering, they generalize previously published work on variational filtering and extend currently available methods for speeding up stochastic approximations in Bayesian filtering. In particular, the free-form nature of the VB approximation allows optimal selection of moments which summarize the particles. Other Bayesian filtering schemes are developed by replacing the marginalization operator in Bayesian filtering with VB-marginals. This leads to further computational savings at the cost of quality of approximation. The performance of the various VB filtering schemes is illustrated in the context of a Gaussian model with a nonlinear substate, and a hidden Markov model.