With the deepening of degradation, the stability and reliability of the degrading system usually becomes poor, which may lead to random jumps occurring in the degradation path. A non-homogeneous jump diffusion process model is introduced to more accurately capture this type of degradation. In this paper, the proposed degradation model is translated into a state–space model, and then the Monte Carlo simulation of the state dynamic model based on particle filtering is employed for predicting the degradation evolution and estimating the remaining useful life (RUL). In addition, a general model identification approach is presented based on maximization likelihood estimation (MLE), and an iterative model identification approach is provided based on the expectation maximization (EM) algorithm. Finally, the practical value and effectiveness of the proposed method are validated using real-world degradation data from temperature sensors on a blast furnace wall. The results demonstrate that our approach provides a more accurate and robust RUL estimation compared to CNN and LSTM methods, offering a significant contribution to enhancing predictive maintenance strategies and operational safety for systems with complex, non-monotonic degradation patterns.