User`s guide

Computing Model Uncertainty
Computing the covariance matrix is based on the assumption that the model
structure gives the correct description of the system dynamics. For models
that include a disturbance model H, a correct uncertainty estimate assumes
that the model produces w h ite residuals. To determine w hether you can trust
the estimated model uncertainty values, perform residual analysis tests
on your model, as described in “Using Residual Analysis Plots to Validate
Models” on page 8-16. If your model passes residual analysis tests, there is a
good chance that the true system lies w ithin the confi dence interval and any
parameter uncertainties results fromrandomdisturbancesintheoutput.
Inthecaseofoutput-errormodels,wherethenoisemodelH is fixe d to
1,
computing the covariance m atrix does not assume that the residuals are
white. Instead, the covariance is estimated based on the estimated color of the
residual correlations. This estimation of the noise color is also performed for
state-space models with K=
0, which is equivalent to an output-error model.
Viewing Model Uncer tainty Information
You can view the following uncertainty information from linear and nonlinear
grey-box mo de ls:
• Uncertainties o f estimated parameters.
Type
present(model) at the prompt, where model represents the name of
alinearornonlinearmodel.
• Confidence intervals on the linear model plots, including step-response,
impulse-response, Bode, and pole-zero plots.
Confidence intervals are computed based on the variability in the model
parameters. For information about displaying confidence intervals, see the
corresponding plot section.
• Covariance matrix of the estimated parameters in linear and nonlinear
grey-box mo de ls.
Type
model.CovarianceMatrix at the prompt, where mod el represents the
name of the model object.
• Estimated standard deviations of polynomial coefficients or state-space
matrices
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