Parameter Estimation for Nonlinearly Parameterized Gray-Box Models

Many applications involve gray-box models, where the structure of the dynamics as a function of the parameters is known, but the values of the parameters are unknown. Nonlinear estimation algorithms, such as the extended Kalman filter (EKF) and the unscented Kalman filter (UKF), are typically applied to these problems. As an alternative approach, this paper uses retrospective cost model refinement (RCMR), which optimizes a retrospective cost function to update the gain of the estimator. In this paper, we investigate RCMR by estimating a single unknown parameter that may appear nonlinearly in linear and nonlinear systems.