Nonlinear instrument variable methods based on local linear models

The aim of the present study is to derive nonlinear instrument variable methods by using local linear models. Two algorithms to estimate consistent local ARX-models of the system order are presented. A local ARX-model with a regressor of higher order than the system is simulated to estimate an approximately noise-free data set. In the first algorithm this approximately noise-free data is used as estimation data to a local ARX-model of the system order. The second algorithm uses the simulated data as instrument in a local instrument variable method. The algorithms are demonstrated on both simulated and laboratory data