Estimability and dependency analysis of model parameters based on delay coordinates.

Area of Science:

• Dynamical systems theory
• System identification
• Nonlinear dynamics

Background:

• Data-driven system identification estimates model parameters and unobserved variables from time-series data.
• Assessing the uniqueness and redundancy of these estimates is crucial for reliable model-based predictions.
• Existing methods may not fully address the inherent ambiguities in parameter and variable estimation.

Purpose of the Study:

• To investigate the estimability and redundancy of parameters and variables in dynamical system models.
• To develop a method for determining whether unique estimates can be obtained from time-series data.
• To provide insights into the conditions leading to non-unique parameter or variable estimates.

Main Methods:

• Analysis of the null space of the linearized delay coordinates map.
• Application of system identification techniques to dynamical systems.
• Utilizing time-series data from benchmark models.

Main Results:

• The null space of the linearized delay coordinates map provides a definitive criterion for parameter and variable estimability.
• Identified distinct cases corresponding to zero-dimensional, one-dimensional, and two-dimensional null spaces.
• Demonstrated the practical application of the method using the Hindmarsh-Rose model, Colpitts oscillator, and Rössler system.

Conclusions:

• The null space analysis effectively distinguishes between estimable and non-estimable parameters/variables in dynamical systems.
• Understanding null space dimensions is key to identifying potential redundancies and ensuring unique model identification.
• This approach enhances the reliability of data-driven system identification for complex dynamical systems.