Improved Particle Filter Using Clustering Similarity of the State Trajectory with Application to Nonlinear Estimation: Theory, Modeling, and Applications

A clustering similarity particle filter based on state trajectory consistency is presented for the mathematical modeling, performance estimation, and smart sensing of nonlinear systems. Starting from an information fusion model based on the consistency principle of the spatial state trajectory, the predicted observation information of the current particle filter (original trajectory) and future multistage Gaussian particle filter (modified trajectory) are selected as the state trajectories of the sampling particles. Clustering similarity methods are used to measure the state trajectories of the sampling particles and the actual system (reference trajectory). The importance weight of a first-order Markov model is updated with the measurement results. By integrating the targeted compensation scheme of the latest measurement information into the sequential importance sampling process, the adverse effects of the particle degradation phenomenon are effectively reduced. The convergence theorems of the improved particle filter are proposed and proved. The improved filter is applied to practical cases of nonlinear process estimation, economic statistical prediction, and battery health assessment, and the simulation results show that the improved particle filter is superior to traditional filters in estimation accuracy, efficiency, and robustness.