Learn more about System Identification Toolbox

bj - Box-Jenkins (BJ) model estimation

Syntax

m = bj(data,[nb nc nd nf nk]) m = bj(data,[nb nc nd nf nk],'PropertyName',PropertyValue) m = bj(data,m_initial)

Description

m = bj(data,[nb nc nd nf nk]) estimates Box-Jenkins model parameters and their covariances from input-output data. m is an idpoly object. data is a time-domain, single-output iddata object. nb, nc, nd, and nf are orders of the B, C, D, and F polynomials, respectively. nk is the input delay, specified as the number of samples. 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 = bj(data,[nb nc nd nf nk],'PropertyName',PropertyValue) estimates Box-Jenkins model using algorithm options specified by idpoly property name-value pairs. See Algorithm Properties.

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

bj does not support frequency-domain and multiple-output data.

Definitions

The general Box-Jenkins model structure is:

where nu is the number of input channels.

The orders of Box-Jenkins model are defined as follows:

Examples

Estimate parameters of a single-input single-output Box-Jenkins model:

% Load SISO data.
  load iddata1;
% Estimate model parameters
  mbj = bj(z1,[2 2 2 2 1])

Estimate parameters of a multi-input single-output Box-Jenkins model:

% Load MISO data.
  load iddata8;
% Estimate model parameters
  mbj = bj(z8,[[2 1 1] [2 1 2] 1 1 [5 10 15]])

Estimate parameters of a single-input single-output Box-Jenkins model using estimation algorithm properties:

% Generate estimation data using simulation.
  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];
% Estimate model parameters.
  mbj_i = bj(z,[2 2 2 2 1]);
% Repeat the estimation with more iterations.
  mbj = bj(z,mbj_i,'MaxIter',50)
% View the estimation results.
  mbj.EstimationInfo
% Compare initial and refined model parameters.
  compare(z,mbj,mbj_i)

References

Ljung, L. System Identification: Theory for the User, 2nd ed., Upper Saddle River, NJ, Prentice-Hall, 1999. See the chapter on computing the estimate.