Data-Driven Parameter Estimation for Models with Nonlinear Parameter Dependence

摘要

Many models have known structure but unknown parameters. Nonlinear estimation methods, such as the extended Kalman filter (EKF), unscented Kalman filter (UKF), and ensemble Kalman filter (EnKF) are typically applied to these problems by viewing the unknown parameters as constant states. An alternative approach is provided by retrospective cost model refinement (RCMR), which uses an error signal given by the difference between the output of the physical system and the output of the model to update the parameter estimate. The parameter update is based on the retrospective cost function, whose minimizer updates the coefficients of the estimator. The present paper extends RCMR to the case where the model depends nonlinearly on multiple unknown parameters.