User`s guide

3 Linear Model Identification
Options for Initial States
When you use the iterative estimation algorithm PEM to estimate ARMAX,
Box-Jenkins (BJ), Output-Error (OE), you must specify how the algorithm
treats initial states.
This inform a t ion supports the estimation procedures “How to Estimate
Polynom i al Models in the GUI” on page 3-57 and “Usi ng pem to Estimate
Polynomial Models” on page 3-61.
In the System Identification Tool GUI. For ARMAX, OE, and BJ models,
set Initial state to one of the following options:
•
Auto — Autom atically chooses Zero, E stim ate,orBackcast based on the
estimation data. If initial states hav e negligible effect on the prediction
errors, the initial states are set to zero to optimize algorithm performance.
•
Zero — S ets all initia l states to zero.
•
Estimate — Treats the initial states as an unknown vector of param eters
and estimates these states from the da ta.
•
Backcast — Estimates initia l s tates using a smo othing filter.
At the command line. Specify the initial states as an argument in the
model-estimation command. For example, use this command to estimate an
ARMAX model and set the initial states to zero:
m=armax(data,[2 2 2 3],'InitialState','zero')
For a complete list of valu es for t he InitialSt ate model property, see the
idpoly reference p age.
Algorithms for Estimating P olynomial Models
For linear ARX and AR models, you can choose between the ARX and IV
algorithms. ARX implements the least-squares estimation metho d that uses
QR-factorization for ov erdetermined linear equations. IV is the instrumental
variable method. For more information about IV, see the section on
variance-optimal ins truments in System Identification: T heory for the U ser,
Second Edition, by Lennart Ljung, Prentice Hall PTR, 1999.
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