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Kernel Nonlinear Dynamic System Identification Based on Expectation-Maximization Method

This paper develops a kernel nonlinear system identification approach to dual estimation problems. Given the observation model and the corresponding observation sequence, the unknown state transition function is approximated in the reproducing kernel Hilbert space (RKHS), while the corresponding hidden states are also estimated with the unscented Kalman smoother (UKS). To implement the dual estimation, the optimization solution of the proposed kernel expectation-maximization (EM) cost function is approximated based on the unscented transform (UT). Finally, the kernel nonlinear system identification method is applied to the noisy time-series estimation, where the data are generated by the IKEDA chaotic dynamical system with unknown system parameters. The simulation results show that the noisy data's signal-noise ratio (SNR) is improved significantly and is close to the SNR obtained with the accurate system model. Furthermore, the proposed non-parametric approach is compared with the parametric approach and outperforms obviously the parametric approach, even if the parameterized system model is assumed to be known.