Particle Filtering (PF) is used in prognostics applications by reason of its capability of robustly predicting the future behavior of an equipment and, on this basis, its Residual Useful Life (RUL). It is a model-driven approach, as it resorts to analytical models of both the degradation process and the measurement acquisition system. This prevents its applicability to the cases, very common in industry, in which reliable models are lacking. In this work, we propose an original method to extend PF to the case in which an analytical measurement model is not available whereas, instead, a dataset containing pairs "state - measurement" is available. The dataset is used to train a bagged ensemble of Artificial Neural Networks (ANNs) which is, then, embedded in the PF as empirical measurement model. The novel PF scheme proposed is applied to a case study regarding the prediction of the RUL of a structure, which is degrading according to a stochastic fatigue crack growth model of literature.