User`s guide

Commands for Recursive Estimation

You can recursively estimate linear polynomial models, such as ARX,

ARMAX, Box-Jenkins, and Output-Error models. If you are working with

time-series data that contains no inputs and a single output, you can

estimate AR (Auto-Regressive) and ARMA (Auto-Regress iv e Moving Average)

single-output m odels.

Before estimating models using recursive algorithms, you m ust import your

data into the M ATLAB workspace and represent your data in e ither of the

following formats:

• Matrix of the form

[y u]. y represents the output data using one or more

column vectors. Similarly,

u represents the input data using one or more

column vectors.

•

iddata or idfrd object. For more information about creating these objects,

see Chapter 1, “Data Processing”.

The g eneral syntax for recursive estimation commands is as follow s:

[params,y_hat]=command(data,nn,adm,ad g)

params

matrix contains the values of the estimated parameters, w here the

kth row contains the parameters associated with time k,whicharecomputed

using the

data values in the row s up to and including t h e row k.

y_hat contains the predicted output values such that the kth row of y_hat is

computed based on the

data va lues in the r ows u p to and including the ro w k.

Tip y_hat contains the adaptive predictions of the output and is useful for

adaptive ﬁltering applications, such as noise cancelation.

nn speciﬁed the model orders and delay according to the speciﬁcpolynomial

structure of the model. For example,

nn=[na nb nk] for ARX models. For

more inform ation about s pe c ifying polynomi al model orders and delays, see

“Identifying Input-O u tput Polynomial Models” on p age 3-41.

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