Optimized Improvement of Convergency in Least Squares Parameter Estimation of Biomedical Models

Abstract

This paper investigates a method for optimally improving the convergency and stabil ity in the least squares (LS) estimation of model parameters in biological models. When we have to use a strongly correlated input for the identification and we are given only short length of noisy input-output measurement data, as arises in actual ph0ysiological experiments, the LS parameter estimates tend to fluctuate excessively and not to settle in steady-state values for the given data length. We focus on a method of adding nonnegative weighting constants into the diagonal elements of the data covariance matrix, which is normally used to mitigate the ill-conditions of a nearly singular covariance matrix. The aim of this paper is to theoretically describe the effects of the weighting constants on the mean square error (MSE) of the parameter estimates, and clarify the existence of the optimal weighting constant minimizing the MSE. Furthermore, we give a data-adaptive way of determining the optimal value of the weighting constant, which makes use of only available input-output measurement data. The effectiveness of the optimal selection of the weighting constant in the convergency improvement is investigated through both numerical simulations and modell ing of kinetics in diabetes using depancreatized dogs.