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A numerical identifiability test for state-space models--application to optimal experimental design.

M E Hidalgo1, E Ayesa

  • 1Section of Environmental Engineering, CEIT, Po. Manuel Lardizabal, 15, 20018, San Sebastián, Spain.

Water Science and Technology : a Journal of the International Association on Water Pollution Research
|June 2, 2001
PubMed
Summary

This study introduces a mathematical tool for analyzing the identifiability of complex, non-linear systems. The method aids in predicting estimation errors during calibration experiments for models like ASM.

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Area of Science:

  • Systems Biology
  • Mathematical Modeling
  • Control Theory

Background:

  • High-order non-linear systems are common in scientific modeling.
  • Identifiability analysis is crucial for reliable parameter estimation.
  • Existing methods can be complex or computationally intensive.

Purpose of the Study:

  • To present a novel mathematical tool for identifiability analysis.
  • To enable rigorous analysis of estimation errors in calibration experiments.
  • To provide a simulator-implementable, time-discrete approach.

Main Methods:

  • Recursive numerical evaluation of the information matrix.
  • Geometric interpretation of the information matrix for parameter grouping.
  • Application to time-discrete, state-space models.

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Main Results:

  • The proposed tool is easily applicable to high-order non-linear systems.
  • It allows rigorous analysis of average and maximum estimation errors.
  • Demonstrated utility in optimal experimental design for ASM Model No. 1 calibration.

Conclusions:

  • The developed mathematical tool offers a practical approach to identifiability analysis.
  • It enhances the reliability of parameter estimation in complex systems.
  • Facilitates optimal experimental design for biological models.