## Disturbance Model Structure for Process Models

This section describes how to specify a noise model in the estimation procedures Estimate Process Models Using the App and Estimate Process Models at the Command Line.

In addition to the transfer function G, a linear system can include an additive noise term He, as follows:

$y=Gu+He$

where e is white noise.

You can estimate only the dynamic model G, or estimate both the dynamic model and the disturbance model H. For process models, H is a rational transfer function C/D, where the C and D polynomials for a first- or second-order ARMA model.

In the System Identification app, to specify whether to include or exclude a noise model in the Process Models dialog box, select one of the following options from the Disturbance Model list:

• None — The algorithm does not estimate a noise model (C=D=1). This option also sets Focus to Simulation.

• Order 1 — Estimates a noise model as a continuous-time, first-order ARMA model.

• Order 2 — Estimates a noise model as a continuous-time, second-order ARMA model.

At the command line, specify the disturbance model using the procestOptions option set. For example, use this command to estimate a first-order transfer function and a first-order noise model:

opt = procestOptions;
opt.DisturbanceModel = 'arma1';
model = procest(data, 'P1D', opt);

For a complete list of values for the DisturbanceModel model property, see the procestOptions reference page.