The accurate estimation of the remaining useful life plays a crucial role in ensuring the reliability and efficiency of turbofan engines. In this study we address this objective by resorting to a virtual health indicator, previously developed by the authors for the estimation of the turbofan state of health, which is propagated in the future for estimating the engine end of life. The proposed approach consists in a combination of a multi-layer perceptron whose parameters are identified by a particle filter, in which the network act as a surrogate model for the hidden degradation state. The model is initialized on the basis of known degradation trajectories, and is recursively updated by the particle filter when new observations are available, providing flexibility to the method. To assess the effectiveness of the proposed approach, a comparison is made with a commonly used combination in the literature, which utilises a particle filter and a sum of two exponential functions. The results of the comparison demonstrate that the new approach achieves at least comparable results, and in the majority of cases, it outperforms the usual combination.