Parameter sensitivity, estimation and convergence: an information approach

Convergence rates are analyzed for Recursive Prediction (Output) Error Methods (RPEM) in the identification of linear state-space systems from (noisy) impulse response data) RPEM algorithms are derived which are suitable for the identification of the parameters in arbitrary state-space structures. Deterministic and stochastic versions of these identification algorithms are presented. These two classes indicate the number of realizations used in the identification, not the presence or absence of noise. The convergence analysis uses the eigen-information of the correlation matrix (really its inverse, the Fisher information matrix) for a chosen parameterization. This analysis explains why various state-space structures have different convergence properties, 1.e., why for the same system the estimation processes corresponding to different identification structures converge at different rates. The eigen-information of the parameter information matrix relates the system sensitivity and numerical conditioning in a manner which provides insight into the identification process. The relevant eigen-information is combined in the proposed scalar convergence time constant +. One important result is that identification of the usually identified direct form II parameters (the standard ARMA parameters) does not necessarily yield the fastest parameter set convergence for the system being identified. Identification from arbitrary input is also briefly considered, as is identification when the model order is different from the “true” system order.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Electrical Engineering

Department dc:contributor.department

Electrical Engineering

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

1990

Author dc:creator

• DeBrunner, Victor Earl

Chair dc:contributor.committeechair

• Beex, A. A. Louis

Committee members dc:contributor.committeemember

• Beattie, Christopher A.
• Bingular, Stanoje P.
• Lindner, Douglas K.
• Riad, Sedki Mohamed

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Language dc:language.iso

en

Dc Identifier Other

etd-10142005-135736

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/39893