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Numerical parameter identifiability and estimability: Integrating identifiability, estimability, and optimal sampling design. (English) Zbl 0581.93017
The authors suggest a common approach based on a least squares technique to investigate model identifiability, estimability and optimal sampling design.
As a starting point the two levels of parameters encountered in the identifiability analysis are emphasized: the ”structural” and ”experimental” parameters, related with system and experiment; the ”observational” parameters, that is some functions of the previous ones which can be uniquely identified by means of the observations.
A least squares procedure is employed, based on a set of observations generated at initial parameter estimates, then the Jacobian matrix of the equations involved is constructed such that the parameters appear structured into three groups: those that are observable and identifiable, those that are observable but not identifiable, those that are not observable and not identifiable.
It is pointed out, and numerous examples are provided as an illustration, that the correlation matrix provides some information to separate the previous groups and highlights the difficulties that can arise in estimating some parameters, because of the high correlations between them.
Finally, to optimise sampling times, a strategy, which maximises the sensitivity of the sums of square deviations, is chosen to change the parameters to be estimated; this leads to equations very similar to those encountered in the identifiability study.
Reviewer: L.d’Angio

MSC:
93B30 System identification
92Cxx Physiological, cellular and medical topics
93C57 Sampled-data control/observation systems
93B40 Computational methods in systems theory (MSC2010)
65D99 Numerical approximation and computational geometry (primarily algorithms)
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