The Fully Adapted Auxiliary Particle Filter (FA-APF) is a well known Sequential Monte Carlo (SMC) algorithm for computing recursively the filtering pdf in a Hidden Markov Chain (HMC) model. However, in most of cases, the FA-APF cannot be used directly because the required functions are unavailable. To cope with this issue, the Auxiliary Particle Filter (APF) uses Importance Sampling (IS) with two degrees of freedom. APF techniques need an importance distribution and also a reliable approximation of the predictive likelihood. In this paper, we propose a class of SMC algorithms which also try to mimic the FA-APF but which have the advantage not to require any approximation of the predictive likelihood. The performances of our solution as compared to the APF algorithm is provided by simulations