Analysis of errors in parameter estimation with application to physiological systems.

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.