Estimate parameters of ARX or AR model using least squares
sys = arx(data,[na
nb nk])
sys = arx(data,[na
nb nk],Name,Value)
sys = arx(data,[na
nb nk],___,opt)
arx
does not support continuoustime estimations.
Use tfest
instead.
returns an ARX structure polynomial
model, sys
= arx(data
,[na
nb nk]
)sys
, with estimated parameters and covariances
(parameter uncertainties) using the leastsquares method and specified orders
.
estimates
a polynomial model with additional options specified by one or more sys
= arx(data
,[na
nb nk]
,Name,Value
)Name,Value
pair
arguments.
specifies
estimation options that configure the estimation objective, initial
conditions and handle input/output data offsets.sys
= arx(data
,[na
nb nk]
,___,opt
)

Estimation data. Specify 

Polynomial orders.


Estimation options.
Use 
Specify optional
commaseparated pairs of Name,Value
arguments. Name
is
the argument name and Value
is the corresponding value.
Name
must appear inside quotes. You can specify several name and value
pair arguments in any order as
Name1,Value1,...,NameN,ValueN
.

Input delays. For a system with Default: 0 for all input channels 

Transport delays. Specify transport delays as integers denoting delay of a multiple
of the sample time, For a MIMO system with Default: 0 for all input/output pairs 

Specify integrators in the noise channels. Adding an integrator creates an ARIX model represented by: $$A(q)y(t)=B(q)u(tnk)+\frac{1}{1{q}^{1}}e(t)$$ where,$$\frac{1}{1{q}^{1}}$$ is the integrator in the noise channel, e(t).
Default: 

ARX model that fits the estimation data, returned as a discretetime Information about the estimation results and options used is
stored in the
For more information on using 
QR factorization solves the overdetermined set of linear equations that constitute the leastsquares estimation problem.
Without regularization, the ARX model parameters vector θ is estimated by solving the normal equation:
$$\left({J}^{T}J\right)\theta ={J}^{T}y$$
where J is the regressor matrix and y is the measured output. Therefore,
$$\theta ={\left({J}^{T}J\right)}^{1}{J}^{T}y$$.
Using regularization adds a regularization term:
$$\theta ={\left({J}^{T}J+\lambda R\right)}^{1}{J}^{T}y$$
where, λ and R are the regularization constants. See arxOptions
for more information on the
regularization constants.
When the regression matrix is larger than the MaxSize
specified
in arxOptions
, data is segmented
and QR factorization is performed iteratively on these data segments.