| 1. |
- Ljung, Lennart, 1946-, et al.
(författare)
-
Asymptotic Properties of Black-Box Identification of Transfer Functions
- 1984
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- The problem of estimating the transfer function of a linear, stochastic system is considered. The transfer function is parametrized as a black box and no given order is chosen a priori. This means that the model orders may increase to infinity when the number of observed data tends to infinity. The consistency and convergence properties of the resulting transfer function estimates are investigated. Asymptotic expressions for the variances and distributions of these estimates are also derived for the case that the model orders increase. It is shown that the variance of the transfer function estimate at a certain frequency is asymptotically given by the noise-to-signal ratio at that frequency mulliplied by the model-order-to-number-of-data-points ratio.
|
|
| 2. |
|
|
| 3. |
- Ljung, Lennart, 1946-, et al.
(författare)
-
Properties of Non-Parametric Time-Domain Methods for Estimating Transfer Functions
- 1983
-
Ingår i: Proceedings of the 22nd IEEE Conference on Decision and Control. - Linköping : Linköping University. ; , s. 323-324
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- The problem of estimating the transfer function of a linear, stochastic system is considered. The transfer function is parametrized as a black box and no given order is chosen a priori. This means that the model orders may increase to infinity when the number of observed data tends to infinity. The consistency and convergence properties of the resulting transfer function estimates are investigated. Asymptotic expressions for the variances and distributions of these estimates are also derived for the case that the model orders increase. It is shown that the variance of the transfer function estimate at a certain frequency is asymptotically given by the noise-to-signal-ratio at that frequency multiplied by the number-of-estimated parameters to number-of-data-points-ratio. This result is essentially independent of the model structure used.
|
|
| 4. |
|
|
| 5. |
- Yuan, Zhen-Dong, et al.
(författare)
-
Black-Box Identification of Multivariable Transfer Functions : Asymptotic Properties and Optimal Input Design
- 1983
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- The problem of estimating the transfer function of a multivariable linear stochastic system is considered. The transfer function is parametrized as a black box and no order is chosen a priori. This means that the model order may increase to infinity as the number of observed data tends to infinity. The asymptotic covariance of the transfer function estimate is calculated and is found to be independent of the noise model when the model order increases to infinity. The derived expressions are also used to determine optimal ' unprejudiced ' input signals for the identification experiment.
|
|
| 6. |
- Yuan, Zhen-Dong, et al.
(författare)
-
Unprejudiced Optimal Input Design for Identification of Transfer Functions
- 1983
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- The problem to estimate transfer functions of linear systems is considered. The quality of the resulting estimate depends, among other things, on the input used during the identification experiment. We measure the quality using a quadratic norm in the frequency domain. The problem to determine optimal inputs, i.e. inputs that minimize the chosen norm, subject to constrained input variance, has long been studied. We point out that such procedures may involve a prejudice (that the system is to be found in a certain model set) that may have some surprising effects. We discuss how such a prejudice can be reduced by allowing the possibility that the true system cannot be exactly described in the chosen model set. We also calculate explicit expressions for the resulting “unprejudiced” optimal inputs. These expressions relate the signal-to-noise ratio (as a function of frequency) to the chosen weighting function in the quadratic norm. We also point out the role of the employed noise model for the design.
|
|
| 7. |
- Yuan, Zhen-Dong
(författare)
-
Unprejudiced Optimal Open Loop Input Design for Identification of Transfer Functions
- 1984
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- The problem to estimate transfer functions of linear systems is considered. The quality of the resulting estimate depends, among other things, on the input used during the identification experiment. We measure the quality using a quadratic norm in the frequency domain. The problem to determine optimal inputs, i.e. inputs that minimize the chosen norm, subject to constrained input variance, has long been studied. We point out that such procedures may involve a prejudice (that the system is to be found in a certain model set) that may have some surprising effects. We discuss how such a prejudice can be reduced by allowing the possibility that the true system cannot be exactly described in the chosen model set. We also calculate explicit expressions for the resulting “unprejudiced” optimal inputs. These expressions relate the signal-to-noise ratio (as a function of frequency) to the chosen weighting function in the quadratic norm. We also point out the role of the employed noise model for the design.
|
|
| 8. |
- Zhen-Dong, Yuan, et al.
(författare)
-
Optimal Input Design by Frequency Domain Criteria
- 1982
-
Ingår i: Proceedings of the 21st IEEE Conference on Decision and Control. - Linköping : Linköping University. ; , s. 1005-1006
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Some explicit, analytical result on optimal input design for identification of transfer functions are derived. The results are asymptotic as the model order increases. This can be interpreted as a reduction of prejudice in the design; the prejudice being that the system is "known" to belong to a certain low-order model set.
|
|
