基于期望最大化方法的非线性SSM黑箱鲁棒辨识

To address the robust identification problem of nonlinear state space models (SSM) with outliers, missing observations, and unknown state equations, this paper proposes a modeling method based on eigenfunction expansion, Gaussian-process state-space models (GP-SSM), and Student-t distribution. The proposed approach consists of: modeling the state transition function using eigenfunctions and pre-encoding the priors of basis function coefficients via GP-SSM to enhance flexibility; modeling observations as a Student-t distribution with unknown parameters to enhance robustness against outliers; proposing the enhanced particle Gibbs with ancestor sampling (EPGAS) algorithm to adapt to state estimation in scenarios with missing observations; and deriving unknown model parameters based on the expectation maximization (EM) method. The simulation examples and benchmark model test results show that the proposed method has better performance compared to existing literature methods, and can significantly improve the model identification accuracy when there are outliers and missing observations.