System Identification Toolbox

Linear Regression Models

A linear regression model is of the type

(3-65)

where and are measured variables and represents noise. Such models are very useful in most applications. They allow, for example, the inclusion of nonlinear effects in a simple way. The System Identification Toolbox function arx allows an arbitrary number of inputs. You can therefore handle arbitrary linear regression models with arx. For example, if you want to build a model of the type

(3-66)

let

• Data = iddata(y,[ones(size(u)), u, u.^2, u.^3]);
  m= arx(Data,'na',0,'nb',[1 1 1 1],'nk',[ 0 0 0 0])
  

This is formally a model with one output and four inputs, but all the model testing in terms of compare, sim, and resid operate in the natural way for the model (3-65), once the data set Data is defined as above.

Note that when pem is applied to linear regression structures, by default a robustified quadratic criterion is used. The search for a minimum of the criterion function is carried out by iterative search. Normally, use this robustified criterion. If you insist on a quadratic criterion, then set the argument LimitError in pem to zero. Then pem also converges in one step.

nk and InputDelay

Spectrum Normalization and the Sampling Interval