The Variational Bayes (VB) approach is used as a one-step approximation for Bayesian filtering. It requires the availability of moments of the free-form distributional optimizers. The latter may have intractable functional forms. In this contribution, we replace these by appropriate fixed-form distributions yielding the required moments. We address two scenarios of this Restricted VB (RVB) approximation. For the first scenario, an application in identification of HMMs is given. In the second, the fixed-form distribution is generated via Particle Filtering (PF). It is shown that a new approximation of Rao-Blackwellized particle filtering is obtained in this scenario of RVB. Its performance is assessed for a simple nonlinear model. 1. THE VB APPROXIMATION The VB approximation is a deterministic free-form optimization technique. It was first used in off-line inference problems [1] and extended to on-line inference of time-invariant parameters in [2]. The use of VB in Bayesian filtering was first discussed in [3]. The key theory is now reviewed. Theorem 1 (Variational Bayes (VB)) Let f (θ|D) be the posterior distribution of multivariate parameter, θ = [θ ′ 1, θ ′ 2] ′, and ˘ f (θ|D) be an approximate distribution restricted to the set of conditionally independent distributions ˘f (θ|D) = ˘ f (θ1, θ2|D) = ˘ f (θ1|D) ˘ f (θ2|D). (1) The minimum of the Kullback-Leibler divergence ˜f (θ|D) = arg min KL ˘f (θ|D) ||f (θ|D) , (2)

Marginalized particle filtering (MPF), also known as Rao-Blackwellized particle filtering, has been recently developed as a hybrid method combining analytical filters with particle filters. In this paper, we investigate the prospects of this approach in enviromental modelling where the key concerns are nonlinearity, high-dimensionality, and computational cost. In our formulation, exact marginalization in the MPF is replaced by approximate marginalization yielding a framework for creation of new hybrid filters. In particular, we propose to use the MPF framework for on-line tuning of nuisance parameters of ensemble filters. Conditional independence based simplification of the MPF algorithm is proposed for computational rea-sons and its close relation to previously published methods is discussed. Strength of the framework is demonstrated on the joint estimation of the inflation factor, the measurement error variance and the length-scale parameter of covariance localization. It is shown that ac-curate estimation can be achieved with a moderate number of particles. Moreover, this result was achieved with naively chosen proposal densities leaving space for further improvements. 1.