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[thm,yhat,p,phi,psi] = rbj(z,nn,adm,adg,th0,p0,phi,psi)
RBJ Computes estimates recursively for a BOX-JENKINS model.
[THM,YHAT] = RBJ(Z,NN,adm,adg)
Z: The output-input data z=[y u] (single input only!)
NN : NN=[nb nc nd nf nk], The orders and delay of a general
input-output model (see also BJ).
adm: Adaptation mechanism. adg: Adaptation gain
adm='ff', adg=lam: Forgetting factor algorithm, with forg factor lam
adm='kf', adg=R1: The Kalman filter algorithm with R1 as covariance
matrix of the parameter changes per time step
adm='ng', adg=gam: A normalized gradient algorithm, with gain gam
adm='ug', adg=gam: An Unnormalized gradient algorithm with gain gam
THM: The resulting estimates. Row k contains the estimates "in alpha-
betic order" corresponding to data up to time k (row k in Z)
YHAT: The predicted values of the outputs. Row k corresponds to time k
Initial value of parameters(TH0) and of "P-matrix" (P0) can be given by
[THM,YHAT,P] = RBJ(Z,NN,adm,adg,TH0,P0)
Initial and last values of auxiliary data vectors phi and psi are
obtained by [THM,YHAT,P,phi,psi]=RBJ(Z,NN,adm,adg,TH0,P0,phi0,psi0).
See also RARX, RARMAX, ROE, RPEM and RPLR.
| This function calls | |
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function [thm,yhat,p,phi,psi] = rbj(z,nn,adm,adg,th0,p0,phi,psi)
% L. Ljung 10-1-89
% Copyright (c) 1986-98 by The MathWorks, Inc.
% $Revision: 2.3 $ $Date: 1997/12/02 03:43:52 $
if nargin < 4
disp('Usage: MODEL_PARS = RBJ(DATA,ORDERS,ADM,ADG)')
disp(' [MODEL_PARS,YHAT,COV,PHI,PSI] = RBJ(DATA,ORDERS,ADM,ADG,TH0,COV0,PHI,PSI)')
disp(' ADM is one of ''ff'', ''kf'', ''ng'', ''ug''.')
return
end
adm=lower(adm(1:2));
if ~(adm=='ff'|adm=='kf'|adm=='ng'|adm=='ug')
error('The argument ADM should be one of ''ff'', ''kf'', ''ng'', or ''ug''.')
end
[nz,ns]=size(z);
if ns<=1,error('This routine requires an input. For a time series, use RARMAX or RARX instead!'),end
if ns>2,error('This routine is for single input only. Use RPEM instead!'),end
if length(nn)~=5,error('Incorrect number of orders specified! nn = [nb nc nd nf nk]'),end
nb=nn(1);nc=nn(2);nd=nn(3);nf=nn(4);nk=nn(5);nu=1;
if nk<1,error('Sorry, this routine requires nk>0; Shift input sequence if necessary!'),end
d=sum(nn(1:4));
if ns>2,error('Sorry, this routine is for single input only!'),end
ng=nf+nc;
nbm=max([nb+nk-1,ng,nd]);ndm=max(nd,nc);nfm=max([nf,ng,nd]);
tic=nb+1:nb+nc;tif=nb+nc+nd+1:d;
tib=1:nb;tid=nb+nc+1:nb+nc+nd;
ib=nk:nb+nk-1;ibg=1:ng;ibd=nk:nk+nd-1;
ic=nbm+1:nbm+nc;
id=nbm+nc+1:nbm+nc+nd;idc=nbm+nc+1:nbm+nc+nc;
iff=nbm+nc+ndm+1:nbm+nc+ndm+nf;ifg=nbm+nc+ndm+1:nbm+nc+ndm+ng;
ifd=nbm+nc+ndm+1:nbm+nc+ndm+nd;
dm=nfm+nbm+nc+ndm;
i=[ib ic id iff];
if nargin<8, psi=zeros(dm,1);end
if nargin<7, phi=zeros(dm,1);end
if nargin<6, p0=10000*eye(d);end
if nargin<5, th0=eps*ones(d,1);end
if isempty(psi),psi=zeros(dm,1);end
if isempty(phi),phi=zeros(dm,1);end
if isempty(p0),p0=10000*eye(d);end
if isempty(th0),th0=eps*ones(d,1);end
if length(th0)~=d, error('The length of th0 must equal the number of estimated parameters!'),end
[th0nr,th0nc]=size(th0);if th0nr<th0nc, th0=th0';end
p=p0;th=th0;
if adm(1)=='f', R1=zeros(d,d);lam=adg;end
if adm(1)=='k', [sR1,SR1]=size(adg);
if sR1~=d | SR1~=d,error('The R1 matrix should be a square matrix with dimension equal to number of parameters!'),end
R1=adg;lam=1;
end
if adm(2)=='g', grad=1;else grad=0;end
for kcou=1:nz
yh=phi(i)'*th;
epsi=z(kcou,1)-yh;
if ~grad,K=p*psi(i)/(lam + psi(i)'*p*psi(i));
p=(p-K*psi(i)'*p)/lam+R1;
else K=adg*psi(i);end
if adm(1)=='n', K=K/(eps+psi(i)'*psi(i));end
th=th+K*epsi;
c=fstab([1;th(tic)])';f=fstab([1;th(tif)])';d=[1;th(tid)];
th(tic)=c(2:nc+1);th(tif)=f(2:nf+1);g=conv(f,c);%HIT*********
w=th([tib tif])'*phi([ib iff]);
util=d'*[z(kcou,2);phi(ibd)]-g'*[0;psi(ibg)];
if nf>0
wtil=d'*[w;-phi(ifd)]+g'*[0;psi(ifg)];
end
v=z(kcou,1)-w;
epsilon=v-th([tic tid])'*phi([ic id]);
if nc>0
epstil=c'*[epsilon;-psi(ic)];end
if nd>0
vtil=c'*[v;psi(idc)];
end
phi(2:dm)=phi(1:dm-1);psi(2:dm)=psi(1:dm-1);
if nb>0,phi(1)=z(kcou,2);psi(1)=util;end
if nc>0,phi(ic(1))=epsilon;psi(ic(1))=epstil;end
if nd>0,phi(id(1))=-v;psi(id(1))=-vtil;end
if nf>0,phi(iff(1))=-w;psi(iff(1))=-wtil;end
thm(kcou,:)=th';yhat(kcou)=yh;
end
yhat=yhat';