Title :
A statistical perspective on state-space modeling using subspace methods
Author :
Viberg, Mats ; Ottersten, Björn ; Wahlberg, Bo ; Ljung, Lennart
Author_Institution :
Dept. of Electr. Eng., Linkoping Univ., Sweden
Abstract :
The authors investigate aspects of subspace-based state-space identification techniques from a statistical perspective. They concentrate their efforts on a simple approach which is based on finding the range-space of the observability matrix of a state-space representation. The system description is then found using the shift-invariance property of the observability matrix. It is shown that this results in a consistent system description for multivariable output-error models if the measurement noise is white in time and independent from output to output. The asymptotic covariance of the estimated poles of the system is also derived. In the test case studied, the subspace technique performs comparably with the statistically efficient PE (prediction error) method, whereas the instrumental variable method does notably worse. Hence, the subspace technique may be a strong candidate for determining initial values for the optimization in the efficient PE method
Keywords :
identification; matrix algebra; modelling; observability; poles and zeros; state-space methods; statistics; asymptotic covariance; estimated poles; instrumental variable; measurement noise; multivariable output-error models; observability matrix; prediction error; range-space; shift-invariance property; state-space identification; state-space modeling; statistical perspective; subspace methods; white noise; Covariance matrix; Instruments; Maximum likelihood estimation; Noise measurement; Nonlinear filters; Observability; Optimization methods; Performance evaluation; Signal processing; State-space methods; Statistical analysis; System identification; Testing; Time measurement; White noise;
Conference_Titel :
Decision and Control, 1991., Proceedings of the 30th IEEE Conference on
Conference_Location :
Brighton
Print_ISBN :
0-7803-0450-0
DOI :
10.1109/CDC.1991.261612