State space model identification with data correlation

It is proved that a certain sample auto- and cross-correlation Hankel matrix can be used to develop an effective state-space model identification procedure. By incorporating data correlation with a state-space model identification method, identification bias which is inherent in using the singular value decomposition of a noise corrupted Hankel data matrix can be significantly reduced. The proposed new identification procedure is different from other state-space identification methods which use correlation or covariance matrices since the input excitation signals are not limited to a white Gaussian noise or an impulse. These inputs can be any time functions as long as the persistent excitation condition is satisfied