System Identification Toolbox

Data Representation and Nonparametric Model Estimation

This and the following sections give an introduction to the basic functions in the System Identification Toolbox. Not all of the options available when using the functions are described here; see the Function Reference chapter and the online Help facility.

Data Representation

The observed output and input signals, and , are represented as column vectors y and u. Row k corresponds to sample number k. For multivariable systems, each input (output) component is represented as a column vector, so that u becomes an N-by-nu matrix (N = number of sampled observations, nu = number of input channels). The output-input data is collectively represented in the iddata format. This is the basic object for dealing with signals in the toolbox. It is used by most of the commands. It is created by

• Data = iddata(y,u,Ts)
  

where y is a column vector or an N-by-ny matrix. The columns of y correspond to the different output channels. Similarly u is a column vector or an N-by-nu matrix containing the signals of the input channels. Ts is the sampling interval. This construction is sufficient for almost all purposes.

The data is then plotted by plot(Data) and portions of the data record are selected as in

• ze = Data(1:300) 
  

The signals in the output channels are retrieved by Data.OutputData or for short, Data.y. Similarly the input signals are obtained by Data.InputData or Data.u.

For a time series (no input channels) use Data = iddata(y), or let u = [ ]. An iddata object can also contain just an input, by letting y = [ ].

The sampling interval can be changed by set(Data,'Ts',0.3) or, simpler, by

• Data.Ts = 0.3
  

More details about the iddata object is given at the end of this section.

Subspace Methods for Estimating State-Space Models

Correlation Analysis