State-space model identification with data correlation

Abstract

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 to an impulse. These inputs can be any time functions provided the persistent excitation condition is satisfied