Grove T M, Bekey G A, Haywood L J
Am J Physiol. 1980 Nov;239(5):R390-400. doi: 10.1152/ajpregu.1980.239.5.R390.
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.
分析了应用于生理系统的参数估计的准确性。分析方法适用于利用输出误差平方最小化的程序和非线性动态系统模型。描述了估计误差的三个主要来源：1）测量误差，2）建模误差，3）优化误差。测量误差会影响用于系统输出、模型输入和模型非估计参数的值。建模误差是由于未能充分描述系统结构以及模型方程的数字计算机解中出现的数值误差。在标称解区域使用泰勒级数展开进行线性化，以根据每个误差源的协方差矩阵获得参数估计协方差矩阵的表达式。该分析应用于根据呼吸测量估计心输出量的示例。结果表明，系统可识别性分析不足以确保获得可用的估计值，系统误差分析对于评估参数估计技术的有用性至关重要。
