Identification of LPV output-error and Box-Jenkins models via optimal refined instrumental variable methods

Identification of Linear Parameter-Varying (LPV) models is often addressed in an Input-Output (IO) setting. However, statistical properties of the available algorithms are not fully understood. Most methods apply auto regressive models with exogenous input (ARX) which are unrealistic in most practical applications due to their associated noise structure. A few methods have been also proposed for Output Error (OE) models, however it can be shown that the estimates are not statistically efficient. To overcome this problem, the paper proposes a Refined Instrumental Variable (RIV) method dedicated to LPV Box-Jenkins (BJ) models where the noise part is an additive colored noise. The statistical performance of the algorithm is analyzed and compared with existing methods.