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[thm,yhat,p,phi,psi] = rarmax(z,nn,adm,adg,th0,p0,phi,psi)
RARMAX Computes estimates recursively for an ARMAX model.
[THM,YHAT] =RARMAX(Z,NN,adm,adg)
Z: The output-input data z=[y u] (single input only!)
NN : NN=[na nb nc nk], The orders and delay of an ARMAX
input-output model (see also ARMAX)
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 output. Row k corresponds to time k.
Initial value of parameters(TH0) and of "P-matrix" (P0) can be given by
[THM,YHAT,P] = RARMAX(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]=RARMAX(Z,NN,adm,adg,TH0,P0,phi0,psi0).
See also RARX, ROE, RBJ, RPEM and RPLR.
| This function calls | This function is called by |
|---|---|
function [thm,yhat,p,phi,psi] = rarmax(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 03:43:51 $
if nargin < 4
disp('Usage: MODEL_PARS = RARMAX(DATA,ORDERS,ADM,ADG)')
disp(' [MODEL_PARS,YHAT,COV,PHI,PSI] = RARMAX(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);[ordnr,ordnc]=size(nn);
if ns>2,error('This routine is for single input only. Use RPEM instead!'),end
if ns==1, if ordnc~=2;error('For a time series nn should be [na nc]!'),end
else if ordnc~=4, error('the argument nn should be [na nb nc nk]!'),end,end
if ns==1,na=nn(1);nb=0;nc=nn(2);nk=1;
else na=nn(1);nb=nn(2);nc=nn(3);nk=nn(4);nu=1;
end
if nk<1,error('Sorry, this routine requires nk>0; Shift input sequence if necessary!'),end
d=na+nb+nc;
if ns>2,error('Sorry, this routine is for single input only!'),end
if ns==1,nb=0;end
if nb==0,nk=1;end
nam=max([na,nc]);nbm=max([nb+nk-1,nc]);
tic=na+nb+1:na+nb+nc;
ia=1:na;iac=1:nc;
ib=nam+nk:nam+nb+nk-1;ibc=nam+1:nam+nc;
ic=nam+nbm+1:nam+nbm+nc;
iia=1:nam-1;iib=nam+1:nam+nbm-1;iic=nam+nbm+1:nam+nbm+nc-1;
dm=nam+nbm+nc; if nb==0,iib=[];end
ii=[iia iib iic];i=[ia ib ic];
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;
if nc>0,c=fstab([1;th(tic)])';else c=1;end
th(tic)=c(2:nc+1);
epsilon=z(kcou,1)-phi(i)'*th;
if nb>0,zb=[z(kcou,2),-psi(ibc)'];else zb=[];end
ztil=[[z(kcou,1),psi(iac)'];zb;[epsilon,-psi(ic)']]*c;
phi(ii+1)=phi(ii);psi(ii+1)=psi(ii);
if na>0,phi(1)=-z(kcou,1);psi(1)=-ztil(1);end
if nb>0,phi(nam+1)=z(kcou,2);psi(nam+1)=ztil(2);end
if nb==0,zc=ztil(2);else zc=ztil(3);end
if nc>0,phi(nam+nbm+1)=epsilon;psi(nam+nbm+1)=zc;end
thm(kcou,:)=th';yhat(kcou)=yh;
end
yhat=yhat';