A particle filter (PF) is shown to be more accurate than non-linear least squares (NLLS) and an unscented Kalman filter (UKF) for predicting the remaining useful life (RUL) and time until end of discharge voltage (EODV) of a Lithium-ion battery. The three algorithms, i.e. PF, UKF, and NLLS track four states with correct initial estimates of the states and 5% variation on the initial state estimates. The four states are data-driven, equivalent circuit properties or Lithium concentrations and electroactive surface areas depending on the model. The more accurate prediction performance of PF over NLLS and UKF is reported for three Lithium-ion battery models: a data-driven empirical model, an equivalent circuit model, and a physics-based single particle model.