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Please note that the recommended version of Scilab is 2025.0.0. This page might be outdated.
See the recommended documentation of this function
rpem
Recursive Prediction-Error Minimization estimation
Calling Sequence
[w1,[v]]=rpem(w0,u0,y0,[lambda,[k,[c]]])
Arguments
- w0
list(theta,p,l,phi,psi)
where:- theta
[a,b,c] is a real vector of order
3*n
- a,b,c
a=[a(1),...,a(n)], b=[b(1),...,b(n)], c=[c(1),...,c(n)]
- p
(3*n x 3*n) real matrix.
- phi,psi,l
real vector of dimension
3*n
Applicable values for the first call:
- u0
real vector of inputs (arbitrary size). (
u0($)
is not used by rpem)- y0
vector of outputs (same dimension as
u0
). (y0(1)
is not used by rpem).If the time domain is
(t0,t0+k-1)
theu0
vector contains the inputsu(t0),u(t0+1),..,u(t0+k-1)
andy0
the outputsy(t0),y(t0+1),..,y(t0+k-1)
Optional arguments
- lambda
optional argument (forgetting constant) choosed close to 1 as convergence occur:
lambda=[lambda0,alfa,beta]
evolves according to :lambda(t)=alfa*lambda(t-1)+beta
with
lambda(0)=lambda0
- k
contraction factor to be chosen close to 1 as convergence occurs.
k=[k0,mu,nu]
evolves according to:k(t)=mu*k(t-1)+nu
with
k(0)=k0
.- c
Large argument.(
c=1000
is the default value).
Outputs:
- w1
Update for
w0
.- v
sum of squared prediction errors on
u0, y0
.(optional).In particular
w1(1)
is the new estimate oftheta
. If a new sampleu1, y1
is available the update is obtained by:[w2,[v]]=rpem(w1,u1,y1,[lambda,[k,[c]]])
. Arbitrary large series can thus be treated.
Description
Recursive estimation of arguments in an ARMAX model. Uses Ljung-Soderstrom recursive prediction error method. Model considered is the following:
y(t)+a(1)*y(t-1)+...+a(n)*y(t-n)= b(1)*u(t-1)+...+b(n)*u(t-n)+e(t)+c(1)*e(t-1)+...+c(n)*e(t-n)
The effect of this command is to update the estimation of
unknown argument theta=[a,b,c]
with
a=[a(1),...,a(n)], b=[b(1),...,b(n)], c=[c(1),...,c(n)]
.
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