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The problem of separating a superposition of different, simultaneous signals from their mixture appears very frequently in various fields of engineering, such as speech processing, telecommunications, biomedical imaging and financial data analysis. In this thesis, we will confront the problem of source separation in the field of astrophysics, where the contributions of various Galactic and extra-Galactic components need to be separated from a set of observed noisy mixtures. Most of the previous work on the problem perform a blind separation, assume noiseless models, and in the few cases when noise is taken into account it is generally assumed to be Gaussian and space-invariant. Our objective is to study a novel technique named particle filtering, and implement it for the non-blind solution of the source separation problem. Particle filtering is an advanced Bayesian estimation method which can deal with non-Gaussian and nonlinear models, and additive space-varying noise, in the sense that it is a generalization of the Kalman Filter. In this work, particle filters are utilized with objectives of both noise filtering and separation of signals: this approach is extremely flexible, as it is possible to exploit the available a-priori information about the statistical properties of the sources through the Bayesian theory. Especially in case of low SNR, our simulations show that the output quality of the separated signals is better than that of ICA, which is one of the most widespread methods for source separation. On the other hand, since a wide set of parameters, which can take from a large range of values, has to be initialized, the use of this approach needs extensive experimentation and testing.