AJP - Regulatory, Integrative and Comparative Physiology, Vol 239, Issue 5 390-R400, Copyright © 1980 by American Physiological Society
Analysis of errors in parameter estimation with application to physiological systems
T. M. Grove, G. A. Bekey and L. J. Haywood
The accuracy of parameter estimation applied to physiological systems is
analyzed. The method of analysis is applicable to procedures utilizing
minimization of squared output error and a nonlinear dynamic system model.
Three major sources of estimation error are described: 1) measurement
error, 2) modeling error, and 3) optimization error. Measurement errors
affect values used for the system output, the model input, and nonestimated
parameters of the model. Modeling errors are due to failure to adequately
describe the structure of the system and to numerical errors that occur in
the digital computer solution of the model equations. Linearization by use
of Taylor series expansions in the region of the nominal solution is used
to obtain an expression for the covariance matrix of the parameter
estimates in terms of the covariance matrix of each error source. The
analysis is applied to the example of cardiac output estimation from
respiratory measurements. The results demonstrate that an analysis of
system identifiability is not sufficient to ensure usable estimates and
that systematic error analysis is essential for assessing the usefulness of
parameter estimation techniques.
