Integrating the error in the independent variable for optimal parameter estimation. Part I: different estimation strategies on academic cases

摘要

Classical approach to the linear - or non-linear - parameter estimation problem deals with three types of variables: the dependent variable, several independent variables and unknown parameters. These are estimated starting from experimental values of the signal. In many inverse heat transfer problems the location of the detectors is usually not perfectly known and the estimated parameters can be severely biased if this is not taken into account. In order to get a better insight into this case, the academic linear least squares problem is revisited for high signal over noise ratio. The independent variable (nominal abscissa) is considered as both a signal and a parameter, which requires the minimization of a modified two terms least squares functional. The stochastic properties of the resulting estimator are reviewed and its efficiency is tested. This technique has been successfully implemented for thermophysical property measurement in a porous medium and is presented in the second part of this article.