Reliable uncertainty evaluation for ODE parameter estimation- A comparison

Abstract

The traceability of measurements to SI units requires a traceable calibration of the measurement devices employed. In the calibration for time-dependent measurements the mathematical model typically consists of a system of ODEs with constant parameters. The calibration then requires the estimation of these parameters from measurements of corresponding trajectories, and the assignment of reliable uncertainties to the obtained parameter estimates. Many approaches to parameter estimation in ODEs are available. However, the evaluation of a reliable uncertainty associated with the corresponding parameter estimates is challenging. The reasons are, for instance, the existence of many local minima, numerical instabilities or the non-identifiability of parameters from the available measurement data. Here we discuss some general approaches to ODE parameter estimation and demonstrate practical issues for the example of calibrating force sensors from shock force measurements. © Published under licence by IOP Publishing Ltd.