System Identification Toolbox™

bj - Estimate parameters of Box-Jenkins model returning idpoly object

Syntax

m = bj(data,orders)
m = bj(data,'nb',nb,'nc',nc,'nd',nd,'nf',nf,'nk',nk)
m = bj(data,orders,'Property1',Value1,'Property2',Value2,...)

Description

bj returns m as an idpoly object with the resulting parameter estimates, together with estimated covariances. The bj function estimates parameters of the Box-Jenkins model structure

using a prediction error method.

data is an iddata object containing the output-input data. Frequency-domain signals are not supported by bj. Use oe instead.

The model orders can be specified by setting the argument orders to

orders = [ nb nc nd nf nk]

The parameters nb, nc, nd, and nf are the orders of the Box-Jenkins model and nk is the delay. Specifically,

The orders can also be defined as property name/property value pairs (...,'nb',nb,...). Alternatively, you can specify the vector as

orders = mi

where mi is an initial Box-Jenkins model (idpoly model).

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.

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', 'Display', 'MaxIter', 'Tolerance', 'LimitError', and 'FixedParameter'.

See Algorithm Properties and the reference pages for idmodel and idpoly for details of these properties and their possible values.

bj does not support multiple-output models. Use a state-space model for this case (see n4sid and pem).

Examples

Here is an example that generates data and stores the results of the startup procedure separately.

B = [0 1 0.5];
C = [1 -1 0.2];
D = [1 1.5 0.7];
F = [1 -1.5 0.7];
m0 = idpoly(1,B,C,D,F,0.1);
e = iddata([],randn(200,1));
u = iddata([],idinput(200)); 
y = sim(m0,[u e]);
z = [y u];
mi = bj(z,[2 2 2 2 1],'MaxIter',0)
m = bj(z,mi,'Maxi',10)
m.EstimationInfo
m = bj(z,m); % Continue if m.es.WhyStop shows that
             % maxiter is reached.
compare(z,m,mi)

Algorithm

bj uses essentially the same algorithm as armax with modifications to the computation of prediction errors and gradients.

See Also

balred

bode