System Identification for Nonlinear Stochastic State-Space Models Using Ensemble Kalman Inversion with Application to Lithium-Ion Batteries

Abstract

Nonlinear state-space system identification has attracted decades of interest, yet remains challenging because of the interplay among unknown parameters, nonlinear dynamics, and latent state variables. Its difficulty increases dramatically when the state and parameter dimensions increase. To address this challenge, we develop an ensemble Kalman inversion (EnKI)-based approach. This approach leverages EnKI to perform maximum a posteriori parameter estimation through successive local Gaussian approximations, enabling an iterative and incremental search for unknown parameters. The search combines Monte Carlo sampling with Kalman-type updates to evolve an ensemble of parameter samples, thereby offering empirical stability and the ability to handle strongly nonlinear models. The EnKI search is coupled with state estimation conditioned on the latest parameter estimates. This enables parameter identification along with latent state recovery. To improve scalability for large datasets, we further develop a cascaded EnKI (CasEnKI) method, which assimilates subdatasets sequentially to accelerate computation. We validate the proposed methods using a lithium-ion battery model with ten state variables and 18 unknown parameters. Simulation results show that the EnKI approach offers high identification accuracy and empirical stability in parameter search. Further, experimental results illustrate the computational efficiency and scalability of the CasEnKI method for large battery datasets.