rpem — RPEM estimation
[w1,[v]]=rpem(w0,u0,y0,[lambda,[k,[c]]])
: a=[a(1),...,a(n)], b=[b(1),...,b(n)], c=[c(1),...,c(n)]
: list(theta,p,phi,psi,l) where:
[a,b,c] is a real vector of order 3*n
(3*n x 3*n) real matrix.
real vector of dimension 3*n
During the first call on can take:
theta=phi=psi=l=0*ones(1,3*n). p=eye(3*n,3*n)
real vector of inputs (arbitrary size) (if no input take u0=[ ]).
vector of outputs (same dimension as u0 if u0 is not empty). (y0(1) is not used by rpem).
If the time domain is (t0,t0+k-1) the u0 vector contains the inputs
u(t0),u(t0+1),..,u(t0+k-1) and y0 the outputs
y(t0),y(t0+1),..,y(t0+k-1)
Recursive estimation of parameters 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 parameter theta=[a,b,c] with
a=[a(1),...,a(n)], b=[b(1),...,b(n)], c=[c(1),...,c(n)].
optional parameter (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
kcontraction 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.
clarge parameter.(c=1000 is the default value).