Optimally robust system identification of systems subject to amplitude-bounded stochastic disturbances

In this paper it is shown that log cos(/spl pi/x/(2C)) is the optimally robust criterion function for prediction error methods with respect to amplitude-bounded stochastic disturbances. This criterion function minimizes the maximum asymptotic covariance matrix of the parameter estimates for the fami...

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Bibliographic Details
Published inIEEE transactions on automatic control Vol. 43; no. 7; pp. 947 - 953
Main Author Hjalmarsson, H.
Format Journal Article
LanguageEnglish
Published New York, NY IEEE 01.07.1998
Institute of Electrical and Electronics Engineers
Subjects
Amplitude estimation
Applied sciences
Computer science; control theory; systems
Control theory. Systems
Covariance matrix
Errors
Exact sciences and technology
Functions
Identification
Least squares approximations
Matrix algebra
Minimax techniques
Modelling and identification
Noise robustness
Parameter estimation
Prediction error methods
Random processes
Robust estimation
Robustness (control systems)
SRA - ICT
SRA - Informations- och kommunikationsteknik
Statistics
Stochastic processes
Stochastic systems
System identification
Technological innovation
Parameter estimation
Prediction error method
Least squares method
Minimax criterion
Worst case method
Optimality criterion
Amplitude distribution
Identification
Robustness
Asymptotic approximation
Covariance matrix
Stochastic system
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Summary:In this paper it is shown that log cos(/spl pi/x/(2C)) is the optimally robust criterion function for prediction error methods with respect to amplitude-bounded stochastic disturbances. This criterion function minimizes the maximum asymptotic covariance matrix of the parameter estimates for the family of innovations of the systems which are amplitude bounded by the constant C. Furthermore, the stochastic worst case performance of the estimate corresponding to the criterion function log cos(/spl pi/x/(2C)) is better than the worst case performance of the least squares estimate even if the constant C is chosen larger than the actual amplitude bound on the innovations. In addition to its favorable properties in a stochastic setting, this criterion function also generates estimates which are unfalsified in a deterministic framework.
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ISSN:0018-9286
DOI:10.1109/9.701094