This paper presents a novel prognostic method that allows a proper characterization of the uncertainty associated with the evolution in time of nonlinear dynamical systems. The method assumes a state-space representation of the system, as well as the availability of particle-filtering-based estimates of the state posterior density at the moment in which the prognostic algorithm is executed. Our proposal significantly improves all particle-filtering-based prognosis frameworks currently available in two main aspects. First, it provides a correction for the expression that is used for the computation of the Time-of Failure (ToF) probability mass function in the context of online monitoring schemes. Secondly, it presents a method for improved characterization of the tails of the ToF probability mass function via sequential propagation of sigma-points and the computation of Gaussian Mixture Models (GMMs). The proposed algorithm is tested and validated using experimental data related to the problem of Lithium-Ion battery State-of-Charge prognosis. (C) 2016 Elsevier Ltd. All rights reserved.