System Identification Toolbox™

pe - Prediction errors associated with model and data set

Syntax

e = pe(m,data)
[e,x0] = pe(m,data,init)

Description

data is the output-input data set, given as an iddata object, and m is any idmodel or idnlmodel object. Both time-domain and frequency-domain data are supported, and data can also be an idfrd object.

e is returned as an iddata object, so that e.OutputData contains the prediction errors that result when model m is applied to the data.

The argument init determines how to deal with the initial conditions:

• init = 'e(stimate)' means that the initial state is chosen so that the norm of prediction error is minimized. This initial state is returned as x0.

• init = `d(elayexpand)': Same as 'estimate', but for a model with nonzero InputDelay, the delays are first converted to explicit model delays (using inpd2nk) so that they are contained in x0.

• init = 'z(ero)' sets the initial state to zero.

• init = 'm(odel)' uses the model's internally stored initial state.

• init = x0i, where x0i is a column vector of appropriate dimension, uses that value as initial state. For multiexperiment data, x0i may be a matrix whose columns give different initial states for each experiment. For a continuous-time model m, x0 is the initial state for this model. Any modifications of the initial state that sampling might require are automatically handled. If m has a non-zero InputDelay, and you need to access the values of the inputs during this delay, you must first apply inpd2nk(m). If m is continuous in time, it must first be sampled before inpd2nk can be applied.

If init is not specified for linear models, its value is determined, as follows:

• If m.InitialState is 'Estimate', 'Backcast', and 'Auto', init = 'Estimate'.

• If m.InitialState is 'Zero', init = 'zero'.

• If m.InitialState is 'Model' or 'Fixed', init = 'model'. For idss, idproc, and idgrey models, init corresponds to the m.x0 values. For other linear models, init = 'zero'.

If init is not specified for idnlgrey models, init = 'Model' is the default. The values and their estimation behavior are inherited from m.InitialStates.

If init is not specified for idnlarx models, init = 'Estimate' is the default. This corresponds to the first few samples of predicted outputs exactly matching the first few output samples in the data set.

If init is not specified for idnlhw models, init = 'Estimate' is the default. This computes initial states by minimizing the prediction errors over the available data range.

The output argument x0 is the value of the initial state used. If data contains several experiments, x0 is a matrix containing the initial states from each experiment.

See Also

operspec(idnlhw)

pem