Optimal nonuniform sampling interval and test-input design for identification of physiological systems from very limited data

Optimal design of test-inputs and sampling intervals in experiments for linear system identification is treated as a nonlinear integer optimization problem. The criterion is a function of the Fisher information matrix, the inverse of which gives a lower bound for the covariance matrix of the parameter estimates. Emphasis is placed on optimum design of nonuniform data sampling intervals when experimental constraints allow only a limited number of discrete-time measurements of the output. A solution algorithm based on a steepest descent strategy is developed and applied to the design of a biologic experiment for estimating the parameters of a model of the dynamics of thyroid hormone metabolism. The effects on parameter accuracy of different model representations are demonstrated numerically, a canonical representation yielding far poorer accuracies than the original process model for nonoptimal sampling schedules, but comparable accuracies when these schedules are optimized. Several objective functions for optimization are compared. The overall results indicate that sampling schedule optimization is a very fruitful approach to maximizing expected parameter estimation accuracies when the sample size is small.