Premium
Black‐box identification of mimo transfer functions: Asymptotic properties of prediction error models
Author(s) -
Zhu YuCal
Publication year - 1989
Publication title -
international journal of adaptive control and signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.73
H-Index - 66
eISSN - 1099-1115
pISSN - 0890-6327
DOI - 10.1002/acs.4480030406
Subject(s) - transfer function , mathematics , mimo , covariance , covariance matrix , control theory (sociology) , algorithm , computer science , statistics , beamforming , control (management) , artificial intelligence , electrical engineering , engineering
Identification of multi‐input/multi‐output (MIMO) transfer functions is considered. The transfer function matrix is parametrized as black‐box models which have certain shift properties; no structure or order is chosen a priori. In order to obtain a good transfer function estimate, we allow the order of the model to increase to infinity as the number of data tends to infinity. The expression of asymptotic covariance of the transfer function estimates is derived, which is asymptotic both in the number of data and in the model order. The result indicates that the joint covariance matrix of the transfer function estimates of the process and of the noise filter is proportional to the (generalized) ratio of output noise to imput signal; the factor of proportionality is the ratio of model order to number of data. The result is independent of the particular model structure used. This result is the MIMO extension of the theory of Ljung. The application of this theory for defining the upper bounds of identification errors is highlighted.