Set inversion via interval analysis for nonlinear bounded-error estimation
Automatica (Journal of IFAC) - Special section on fault detection, supervision and safety for technical processes
Guaranteed nonlinear parameter estimation from bounded-error data via interval analysis
Mathematics and Computers in Simulation
System identification (2nd ed.): theory for the user
System identification (2nd ed.): theory for the user
Guaranteed robust nonlinear estimation with application to robot localization
IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews
Brief paper: Rigorous parameter reconstruction for differential equations with noisy data
Automatica (Journal of IFAC)
SIAM Journal on Scientific Computing
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Knowledge-based models are ubiquitous in pure and applied sciences. They often involve unknown parameters to be estimated from experimental data. This is usually much more difficult than for black-box models, only intended to mimic a given input-output behavior. The output of knowledge-based models is almost always nonlinear in their parameters, so that linear least squares cannot be used, and analytical solutions for the model equations are seldom available. Moreover, since the parameters have some physical meaning, it is not enough to find some numerical values of these quantities that are such that the model fits the data reasonably well. One would like, for instance, to make sure that the parameters to be estimated are identifiable. If this is not the case, all equivalent solutions should be provided. The uncertainty in the parameters resulting from the measurement noise and approximate nature of the model should also be characterized. This paper describes how guaranteed methods based on interval analysis may contribute to these tasks. Examples in linear and nonlinear compartmental modeling, widely used in biology, are provided.