| System Identification Toolbox | |
ARX Models
To estimate the parameters 
and 
of the ARX model (3-14), use the function arx.
Here na, nb, and nk are the corresponding orders and delays in (3-15) on page 3-11 that define the exact model structure. The function arx implements the least squares estimation method, using QR-factorization for overdetermined linear equations.
An alternative is to use the Instrumental Variable (IV) method described in connection with (3-39). This is obtained with
which gives an automatic (and approximately optimal) choice of the filters N and M in (3-39). (See the procedure (15.21)-(15.26) in Ljung (1999).)
Both arx and iv4 are applicable to arbitrary multivariable systems. If you have ny outputs and nu inputs, the orders are defined accordingly: na is an ny-by-ny matrix whose i -j entry gives the order of the polynomial that relates past values of 
to the current value of 
(i.e., past values of 
up to 
are used when predicting 
. Similarly, the i -j entries of the ny-by-nu matrices nu and nk, respectively, give the order and delay from input number j when predicting output number i. (See Multivariable ARX Models: The idarx Model and Function Reference for exact details.)
| | Parametric Model Estimation | AR Models | |