Create System object for online parameter estimation of BoxJenkins polynomial model
Use recursiveBJ
command for parameter
estimation with realtime data. If all data necessary for estimation
is available at once, and you are estimating a timeinvariant model,
use the offline estimation command, bj
.
obj = recursiveBJ
obj = recursiveBJ(Orders)
obj = recursiveBJ(Orders,B0,C0,D0,F0)
obj = recursiveBJ(___,Name,Value)
creates
a System
object™ for online parameter estimation of a default singleinput
singleoutput (SISO) BoxJenkins polynomial
model structure. The default model structure has polynomials
of order 1 and initial polynomial coefficient values obj
= recursiveBJeps
.
After creating the object, use the step
command
to update model parameter estimates using recursive estimation algorithms
and realtime data.
specifies
the polynomial orders of the BoxJenkins model to be estimated.obj
= recursiveBJ(Orders
)
specifies
the polynomial orders and initial values of the polynomial coefficients.
Specify initial values to potentially avoid local minima during estimation.
If the initial values are small compared to the default obj
= recursiveBJ(Orders
,B0,C0,D0,F0
)InitialParameterCovariance
property
value, and you have confidence in your initial values, also specify
a smaller InitialParameterCovariance
.
specifies
additional attributes of the BoxJenkins model structure and recursive
estimation algorithm using one or more obj
= recursiveBJ(___,Name,Value
)Name,Value
pair
arguments.
recursiveBJ
creates a System
object for
online parameter estimation of SISO BoxJenkins polynomial models
using a recursive estimation algorithm.
A System object is a specialized MATLAB^{®} object designed specifically for implementing and simulating dynamic systems with inputs that change over time. System objects use internal states to store past behavior, which is used in the next computational step.
After you create a System
object, you use commands to process
data or obtain information from or about the object. System objects
use a minimum of two commands to process data — a constructor
to create the object and the step
command
to update object parameters using realtime data. This separation
of declaration from execution lets you create multiple, persistent,
reusable objects, each with different settings.
You can use the following commands with the online estimation System objects in System Identification Toolbox™:
Command  Description 

step  Update model parameter estimates using recursive estimation algorithms and realtime data.

release  Unlock the System object. Use this command to enable setting of nontunable parameters. 
reset  Reset the internal states of a locked System object to the initial values, and leave the object locked. 
clone  Create another System object with the same object property values. Do not create additional objects using
syntax 
isLocked  Query locked status for input attributes and nontunable properties of the System object. 
Use the recursiveBJ
command to create an
online estimation System
object. Then estimate the BoxJenkins
polynomial model parameters (B
, C
, D
,
and F
) and output using the step
command
with incoming input and output data, u
and y
.
[B,C,D,F,EstimatedOutput] = step(obj,y,u)
For recursiveBJ
object properties, see Properties.
recursiveBJ
System
object properties
consist of readonly and writable properties. The writable properties
are tunable and nontunable properties. The nontunable properties cannot
be changed when the object is locked, that is, after you use the step
command.
Use Name,Value
arguments to specify writable
properties of recursiveBJ
objects during object
creation. After object creation, use dot notation to modify the tunable
properties.
obj = recursiveBJ; obj.ForgettingFactor = 0.99;

Estimated coefficients of polynomial B(q), returned as a vector of real values specified in order of ascending powers of q^{1}.


Estimated coefficients of polynomial C(q), returned as a vector of real values specified in order of ascending powers of q^{1}.


Estimated coefficients of polynomial D(q), returned as a vector of real values specified in order of ascending powers of q^{1}.


Estimated coefficients of polynomial F(q), returned as a vector of real values specified in order of ascending powers of q^{1}.


Initial values for the coefficients of polynomial B(q)
of order If the initial guesses are much smaller than the default
Default: 

Initial values for the coefficients of polynomial C(q)
of order The coefficients in InitialC = [1 0.5 0.5]; all(abs(roots(InitialC))<1) ans = 1 If the initial guesses are much smaller than the default
Default: 

Initial values for the coefficients of polynomial D(q)
of order The coefficients in InitialD = [1 0.9 0.8]; all(abs(roots(InitialD))<1) ans = 1 If the initial guesses are much smaller than the default
Default: 

Initial values for the coefficients of polynomial F(q)
of order The coefficients in InitialF = [1 0.9 0.8]; all(abs(roots(InitialF))<1) ans = 1 If the initial guesses are much smaller than the default
Default: 

Estimated covariance The interpretation of


Covariance of the initial parameter estimates, specified as one of the following:
Use only when
Default: 

Recursive estimation algorithm used for online estimation of model parameters, specified as one of the following values:
Forgetting factor and Kalman filter algorithms are more computationally intensive than gradient and unnormalized gradient methods. However, they have better convergence properties. For information about these algorithms, see Recursive Algorithms for Online Parameter Estimation.
Default: 

Forgetting factor, λ, relevant for parameter estimation, specified as a scalar in the range (0,1]. Suppose that the system remains approximately constant over T_{0} samples. You can choose λ such that: $${T}_{0}=\frac{1}{1\lambda}$$
Typical choices of λ are in the range Use only when
Default: 

Enable or disable parameter estimation, specified as one of the following:
Default: 

Floating point precision of parameters, specified as one of the following values:
Setting
Default: 

Covariance matrix of parameter variations, specified as one of the following:
N is the number of parameters to be estimated.
Kalman filter algorithm treats the parameters as states of a
dynamic system and estimates these parameters using a Kalman filter.
Default: 

Adaptation gain, γ, used in gradient recursive estimation algorithms, specified as a positive scalar.
Specify a large value for
Default: 

Bias in adaptation gain scaling used in the
The normalized gradient algorithm divides the adaptation gain
at each step by the square of the twonorm of the gradient vector.
If the gradient is close to zero, this can cause jumps in the estimated
parameters.
Default: 
Starting in R2016b, instead of using the step
command
to update model parameter estimates, you can call the System
object with
input arguments, as if it were a function. For example, [B,C,D,F,EstimatedOutput]
= step(obj,y,u)
and [B,C,D,F,EstimatedOutput] =
obj(y,u)
perform equivalent operations.
Recursive
Polynomial Model Estimator  bj
 clone
 isLocked
 recursiveAR
 recursiveARMA
 recursiveARMAX
 recursiveARX
 recursiveLS
 recursiveOE
 release
 reset
 step