  Population Monte Carlo (PMC) sampling methods are powerful tools for
approximating distributions of static unknowns given a set of observations.
These methods are iterative in nature: at each step they generate samples from
a proposal distribution and assign them weights according to the importance
sampling principle. Critical issues in applying PMC methods are the choice of
the generating functions for the samples and the avoidance of the sample
degeneracy. In this paper, we propose three new schemes that considerably
improve the performance of the original PMC formulation by allowing for better
exploration of the space of unknowns and by selecting more adequately the
surviving samples. A theoretical analysis is performed, proving the superiority
of the novel schemes in terms of variance of the associated estimators and
preservation of the sample diversity. Furthermore, we show that they outperform
other state of the art algorithms (both in terms of mean square error and
robustness w.r.t. initialization) through extensive numerical simulations.
