Methods for system identification are presented using model predictive control to frame a gray-box parameterized state space model. System parameters are identified using an optimization procedure to minimize a first error cost function within a range of filtered training data. Disturbances are accounted for using an implicit integrator within the system model, as well as a parameterized Kalman gain. Kalman gain parameters are identified using an optimization procedure to minimize a second error cost function within a range of non-filtered training data. Recursive identification methods are presented to provide model adaptability using an extended Kalman filter to estimate model parameters and a Kalman gain to estimate system states.