A regularized auxiliary particle filtering approach for system state estimation and battery life prediction

System current state estimation (or condition monitoring) and future state prediction (or failure prognostics) constitute the core elements of condition-based maintenance programs. For complex systems whose internal state variables are either inaccessible to sensors or hard to measure under normal operational conditions, inference has to be made from indirect measurements using approaches such as Bayesian learning. In recent years, the auxiliary particle filter (APF) has gained popularity in Bayesian state estimation; the APF technique, however, has some potential limitations in real-world applications. For example, the diversity of the particles may deteriorate when the process noise is small, and the variance of the importance weights could become extremely large when the likelihood varies dramatically over the prior. To tackle these problems, a regularized auxiliary particle filter (RAPF) is developed in this paper for system state estimation and forecasting. This RAPF aims to improve the performance of the APF through two innovative steps: (1) regularize the approximating empirical density and redraw samples from a continuous distribution so as to diversify the particles; and (2) smooth out the rather diffused proposals by a rejection/resampling approach so as to improve the robustness of particle filtering. The effectiveness of the proposed RAPF technique is evaluated through simulations of a nonlinear/non-Gaussian benchmark model for state estimation. It is also implemented for a real application in the remaining useful life (RUL) prediction of lithium-ion batteries.