Parsimonious Model Based Consistent Subspace Identification of Hammerstein Systems Under Periodic Disturbances

The existing results show the applicability of the over-parameterized model based subspace identification method (OPM-like SIM) developed for consistent estimates of Hammerstein systems under completely unknown periodic disturbances. However, it requires to estimate extra parameters and performer a low rank approximation step. Therefore, it may give rise to unnecessarily high variance in parameter estimates, especially using a small and noisy data set. To overcome this corruptive phenomenon, we propose a parsimonious model based SIM to obtain a consistent parameter estimate for Hammerstein systems under completely unknown periodic disturbances. Two parsimonious models instead of OPM have been used to describe the Hammerstein systems, and an orthogonal projection based fixed point iteration method has been proposed to eliminate the disturbance effects and gives a consistent parameter estimate. The avoidance of estimating extra parameters and a low rank approximation step in classical OPM-like SIM has the potential to improve the accuracy and variance properties of the parameter estimates. The effectiveness and merits are demonstrated with strict mathematical proofs, along with simulation examples.