Improved Particle Filter Algorithm Based on the Parallelotope for Nonlinear System State Estimation and its Application on SOC Estimation

To solve the state estimation problem of nonlinear systems with unknown yet bounded noise, this study proposes an improved particle filter algorithm based on the parallelotope algorithm. First, a parallelotope was used to wrap the errors caused by linearization, and the parallelotopes of state, noise, and linear error were obtained using the Minkowski sum to generate a zonotope prediction set. Then, the zonotope was extended by converting it into symmetric half-spaces, and a minimal volume bounding parallelotope was formed and selected as the feasible prediction domain. Furthermore, the particle feasible domain was calculated from the intersection of the observation strip and the predicted feasible domain, and the particle feasible domain was obtained to screen the particles, which makes the parallelotopic feasible domain becomes closer to the real state. Next, based on the criterion of the maximum-a-posteriori (MAP) density function, the particles outside the feasible domain were mapped to the feasible domain, which brought the distribution of particles closer to the real state while maintaining the diversity of the particles. The computational complexity of the algorithm was also studied. Finally, the effectiveness of the proposed algorithm was verified by the state of charge estimation case on the battery experimental platform.