Residual Analysis-Based Model Improvement for State Space Models With Nonlinear Responses

Xun Shen, Jiancang Zhuang

Abstract: This paper concerns the learning problem of state space models with unknown nonlinear responses. A state space model with unknown nonlinear responses has a linear state equation, while the observation equation consists of linear and nonlinear parts. The model structure of the nonlinear part is unknown. This paper uses the neural network model to approximate the unknown nonlinear part of the observation equation. A residual analysis-based algorithm is proposed to iteratively improve the performance of hidden state inference and parameter estimation for state space models with unknown nonlinear responses. The essence of the proposed algorithm is to use the residual of the linear model to learn the unknown nonlinear part. We show that the proposed algorithm can improve the model iteratively by applying the minorization-maximization principle. A numerical example and a battery capacity estimation case study have been conducted to validate the proposed method. The results show that the proposed method can perform better on parameter estimation and hidden state inference than previously developed tools.