Recursive Particle Filter-Based RBF Network on Time Series Prediction of Measurement Data

Most physical phenomena in nature are chaotic or close to chaos. An irregular time series can be generated or measured with a purely deterministic equation of motion in nonlinear and chaotic systems. This paper presents an adaptive state-space particle filtering (PF)-based trained radial basis function (RBF) network for chaotic and nonstationary observation–prediction. The recursive Bayesian filtering algorithm, which uses the particle representation of density function, is adopted to accomplish nonlinear and non-Gaussian state estimation and achieve improved convergence rate and quality of solution. Four sampling importance resampling approaches, namely, multinomial, systematic, stratified, and residual resampling methods, are considered to resolve weight degeneracy. The effectiveness of our proposed methods is investigated using two chaotic time series and three measurement datasets, including the Mackey–Glass time series, Rossler time series, monthly Lake Erie levels, monthly water usage series, and SML2010 data set. The performances are evaluated through an extensive simulation by computing the average mean square error, mean absolute percentage error, and average relative variance metrics. Simulation results show that the proposed PF-based RBF structure can provide more effective and accurate prediction performances compared with the conventional gradient descent, extended Kalman filter (EKF), and decoupled EKF algorithms (DEKF).