System Identification Toolbox

Enumeration of Estimated Parameters

In some cases the parameters of a model are given just as an ordered list. This is the case for m.ParameterVector and also when online information from the minimization routines are given:

• For the input-output model (3-19) or its multi-input variant (3-41), you have the following alphabetical ordering.

Here superscript refers to the input number:

• For a state-space structure, defined by idss the parameters in m.ParameterValues are obtained in the following order. The A matrix is first scanned row by row for free parameters. Then the B matrix is scanned row by row, and so on for the C, D, K, and X0 matrices.
• For a state-space matrix that is defined by idgrey, the ordering of the parameters is the same as in the user-written M-file.

Multivariable ARX models are internally represented in state-space form. The parameter ordering follows the one described above. The ordering of the parameters may, however, not be transparent so it is better to use idarx and arxdata.

Note that the property PName (for Parameter Name) may be useful to help with the bookkeeping in these cases, and when fixing certain parameters using FixedParameter. The routine setpname may be helpful in automatically setting mnemonic parameter names for black-box models.

Interpretation of the Loss Function

Complex-Valued Data