bj
Estimate BoxJenkins polynomial model using time domain data
Syntax
sys = bj(data, [nb
nc nd nf nk])
sys = bj(data,[nb
nc nd nf nk], Name,Value)
sys = bj(data, init_sys)
sys = bj(data, ___, opt)
[sys,ic] = bj(___)
Description
estimates a BoxJenkins polynomial
model, sys
= bj(data
, [nb
nc nd nf nk]
)sys
, using the timedomain data, data
. [nb
nc nd nf nk]
define the orders of the polynomials used
for estimation.
estimates a polynomial model with additional options specified by one or more
sys
= bj(data
,[nb
nc nd nf nk]
, Name,Value
)Name,Value
pair arguments.
estimates
a BoxJenkins polynomial using the polynomial model sys
= bj(data
, init_sys
)init_sys
to
configure the initial parameterization of sys
.
estimates
a BoxJenkins polynomial using the option set, sys
= bj(data
, ___, opt
)opt
,
to specify estimation behavior.
[
returns the estimated initial conditions as an sys
,ic
] = bj(___)initialCondition
object. Use this syntax if you plan to simulate or
predict the model response using the same estimation input data and then compare the
response with the same estimation output data. Incorporating the initial conditions
yields a better match during the first part of the simulation.
Input Arguments

Estimation data.
You cannot use frequencydomain data for estimating BoxJenkins models. 

A vector of matrices containing the orders and delays of the BoxJenkins model. Matrices must contain nonnegative integers.


Estimation options.
Use 

Polynomial model that configures the initial parameterization
of
Use the To specify an initial guess for, say, the C(q)
term of To specify constraints for, say, the B(q)
term of
You can similarly specify the initial guess and constraints for the other polynomials. 
NameValue Arguments
Specify optional pairs of arguments as
Name1=Value1,...,NameN=ValueN
, where Name
is
the argument name and Value
is the corresponding value.
Namevalue arguments must appear after other arguments, but the order of the
pairs does not matter.
Before R2021a, use commas to separate each name and value, and enclose
Name
in quotes.

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 

Logical specifying integrators in the noise channel.
Setting $$y(t)=\frac{B(q)}{F(q)}u(tnk)+\frac{C(q)}{D(q)}\frac{e(t)}{1{q}^{1}}$$ Where, $$\frac{1}{1{q}^{1}}$$ is the integrator in the noise channel,e(t). Default: 
Output Arguments

BJ 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  

A vector of matrices containing the orders and delays of the BoxJenkins model. Matrices must contain nonnegative integers.
 

Estimated initial conditions, returned as an
If opt = bjOptions('InitialCondition','estimate') [sys,ic] = bj(data,[nb nc nd nf nk],opt) 'auto' setting of
'InitialCondition' uses the 'zero'
method when the initial conditions have a negligible effect on the overall
estimationerror minimization process. Specifying
'estimate' ensures that the software estimates values
for ic .
For more information, see 
Examples
More About
Alternatives
To estimate a continuoustime model, use:
References
[1] Ljung, L. System Identification: Theory for the User, Upper Saddle River, NJ, PrenticeHall PTR, 1999.