System Identification Toolbox

Dealing with Data

Extracting information from data is not an entirely straightforward task. In addition to the decisions required for model structure selection and validation, the data may need to be handled carefully. This section gives some advice on handling several common situations.

Offset Levels

When the data have been collected from a physical plant, they are typically measured in physical units. The levels in these raw input and output measurements may not match in any consistent way. This will force the models to waste some parameters correcting the levels.

Typically, linearized models are sought around some physical equilibrium. In such cases offsets are easily dealt with: subtract the mean levels from the input and output sequences before the estimation. It is best if the mean levels correspond to the physical equilibrium, but if such values are not known, use the sample means.

• Data = detrend(Data);
  

Section 14.1 in Ljung (1999) discusses this in more detail. There are situations when it is not advisable to remove the sample means. It could for example be that the physical levels are built into the underlying model, or that integrations in the system must be handled with the right level of the input being integrated.

With the detrend command, you can also remove piece-wise linear trends.

Selecting Model Structures for Multivariable Systems

Outliers and Bad Data; Multi-Experiment Data