System Identification Toolbox

State-Space Structures: Initial Values and Numerical Derivatives

For a structured state-space model it is sometimes difficult to find good initial parameter values at which to start the numerical search for a minimum of (3-38). It is always best to use physical insight, whenever possible, to suggest such values. For random initialization, the command init is useful. Since there is always a risk that the numerical minimization may get stuck in a local minimum, it is advisable to try several different initialization values for .

In the search for the minimum, the gradient of the prediction errors is computed by numerical differentiation. The step-size is determined by the M-file nuderst. In its default version the step-size is simply times the absolute value of the parameter in question (or the number if this is larger). When the model structure contains parameters with different orders of magnitude, try to scale the variables so that the parameters are all roughly the same magnitude. You may need to edit the M-file nuderst to address the problem of suitable step sizes for numerical differentiation.

State-Space Models with Coupled Parameters: the idgrey Model

Examining Models