Robust Linear and Nonlinear Parameter Estimation in the Bounded-Error Context
When estimating the parameters of a model from experimental data, one usually assumes that the error between the measurements and model outputs can be characterized as a stochastic process whose statistics are either known or expressed as a function of parameters to be estimated. There are, however, situations where such a hypothesis cannot be considered as satisfactory. A first example is when nothing is known about the type of distribution of the error and too few data points are available to make it possible to check any statistical assumption on the error from examination of the residuals. A second example is when the essential part of the error between the model outputs and measurements corresponds to the use of a simplified model (e.g. low order linear ordinary differential equation when the system studied is known to be nonlinear and distributed). The error is then deterministic by nature and not suitably described as random.
KeywordsUncertainty Interval Exact Description Regular Data Nonlinear Parameter Estimation Maximal Euclidian Distance
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