Instrumental variables for nonlinearity recovering in block-oriented systems driven by correlated signals

The goal of the paper is to identify the Hammerstein-type systems excited and disturbed by correlated random processes. The problem is semi-parametric in the sense that the nonlinear static characteristic is recovered without prior knowledge about the linear dynamic block, i.e. when its order is unknown. The method is based on the instrumental variables technique, with the instruments generated by input inverse filtering. It is proved that, in contrast to the least-squares-based approach, the proposed algorithm leads to an asymptotically unbiased, strongly consistent estimate. Constructive procedures of instrumental variables generation are given for some popular cases.