In this paper we propose a new methodology for the Bayesian analysis of nonlinear non-Gaussian state space models where the signal is univariate and Gaussian. The novelty is on the development of a proposal density for the joint posterior distribution of parameters and states. We aim to approximate the posterior of the parameters with a mixture of t-densities and to construct a Gaussian density for approximating the density of the states given the parameters and the data. Our approach is an alternative to other recent developments in the literature. We demonstrate that using our proposal density in an independent Metropolis-Hastings procedure is highly efficient. We also show that our method can be faster than competing MCMC methodologies as it is more easily parallelized. Finally our method can be combined with importance sampling and can be used for the fast evaluation of marginal likelihoods.