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oe - Output-error (OE) model parameter estimation

Syntax

m = oe(data,[nb nc nk]) m = oe(data,[nb nc nk],'PropertyName',PropertyValue) m = oe(data,m_initial)

Description

m = oe(data,[nb nc nk]) estimates output-error model parameters and their covariances from input-output data. data is frequency-domain or time-domain iddata, idfrd, or frd object. m is an idpoly object. nb and nc are orders of the B and C polynomials, respectively. nk is the input delay. Orders and delay are scalar for single-input data, and row vectors for multiple-input data with the same size as the number of input channels.

m = oe(data,[nb nc nk],'PropertyName',PropertyValue) estimates Box-Jenkins model using algorithm options specified by idpoly property name-value pairs. See Algorithm Properties.

m = oe(data,m_initial) refines previously estimated model m_initial, which is an idpoly object.

For multiple-input systems, nb, nf, and nk are row vectors with as many entries as there are input channels. Entry number i then describes the orders and delays associated with the ith input.

oe does not support multiple-output models.

Properties

The structure and the estimation algorithm are affected by any property name/property value pairs that are set in the input argument list. Useful properties are 'Focus', 'InitialState', 'InputDelay', 'SearchMethod', 'MaxIter', 'Tolerance', 'LimitError', 'FixedParameter', and 'Display'.

See Algorithm Properties, idpoly, and idmodel for details of these properties and their possible values.

Use a state-space model for this case (see n4sid and pem).

Definitions

Output-Error (OE) Model

The general Output-Error model structure is:

The orders of the Output-Error model are:

Continuous-Time Output-Error Model

If data is continuous-time (frequency-domain) data, oe estimates a continuous-time model with transfer function:

The orders of the numerator and denominator are nb and nf, similar to the discrete-time case. However, the delay nk has no meaning and you should omit it.

Algorithm

Algorithm minimizes prediction errors. oe algorithm is similar to armax, but oe uses slightly different methods for computing prediction errors and gradients.

Examples

Estimating Output-Error (OE) model of the type :

% Use fast sampled data (Ts = 0.001)
% from a plant with bandwidth of about 500 rad/s.
z = iddata(y,u,0.001);
zf = fft(z);
zf.ts = 0;
m = oe(zf,[1 3],'foc',[0 500])