Using horizon estimation and nonlinear optimization for grey-box identification. (June 2015) - Isaksson, Alf J.; Sjöberg, Johan; Törnqvist, David; Ljung, Lennart; Kok, Manon
Abstract : Highlights: (Moving) horizon estimation used for state estimation may be used also for grey-box identification. If there is process noise horizon estimation will lead to biased estimates even in the linear case. In the linear case, bias can be avoided by adding a Riccati equation based term to the objective function. If the process noise enters linearly, and not in the nonlinear states, the bias can still be eliminated. In the general nonlinear case the bias correction term is approximated in an EKF similar fashion. Abstract: An established method for grey-box identification is to use maximum-likelihood estimation for the nonlinear case implemented via extended Kalman filtering. In applications of (nonlinear) model predictive control a more and more common approach for the state estimation is to use moving horizon estimation, which employs (nonlinear) optimization directly on a model for a whole batch of data. This paper shows that, in the linear case, horizon estimation may also be used for joint parameter estimation and state estimation, as long as a bias correction based on the Kalman filter is included. For the nonlinear case two special cases are presented where the bias correction can be determined without approximation. A procedure how to approximate the bias correction for general nonlinear systems is also outlined.