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[thm,yhat,p,phi] = rplr(z,nn,adm,adg,th0,p0,phi)
RPLR Computes PLR estimates recursively for a general model.
[THM,YHAT] = RPLR(Z,NN,adm,adg)
Z: The output-input data z=[y u] (single input only!)
NN : NN=[na nb nc nd nf nk], The orders and delay of a general
input-output model (see also PEM).
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 valued 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] = RPLR(Z,NN,adm,adg,TH0,P0)
Initial and last values of auxiliary data vector phi are
obtained by [THM,YHAT,P,phi]=RPLR(Z,NN,adm,adg,TH0,P0,phi0).
See also RPEM, RARMAX, RARX, RBJ and ROE
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function [thm,yhat,p,phi] = rplr(z,nn,adm,adg,th0,p0,phi)
% L. Ljung 10-1-89
% Copyright (c) 1986-98 by The MathWorks, Inc.
% $Revision: 2.3 $ $Date: 1997/12/02 03:43:59 $
if nargin < 4
disp('Usage: MODEL_PARS = RPLR(DATA,ORDERS,ADM,ADG)')
disp(' [MODEL_PARS,YHAT,COV,PHI] = RPLR(DATA,ORDERS,ADM,ADG,TH0,COV0,PHI)')
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,if length(nn)~=2,error('For a time series nn should be nn = [na nc]!'),end,end
if ns==2,if length(nn)~=6,error('The argument should be nn = [na nb nc nd nf nk]!'),end,end
if ns==2,na=nn(1);nb=nn(2);nc=nn(3);nd=nn(4);nf=nn(5);nk=nn(6);
else na=nn(1);nc=nn(2);nk=1;nb=0;nd=0;nf=0;end
if nk<1,error('Sorry, this routine requires nk>0; Shift input sequence if necessary!'),end
d=na+nb+nc+nd+nf;
if ns>2,error('Sorry, this routine is for single input only!'),end
nbm=nb+nk-1;
tia=1:na;tib=na+1:na+nb;tic=na+nb+1:na+nb+nc;tid=na+nb+nc+1:na+nb+nc+nd;
tif=na+nb+nc+nd+1:d;
ia=tia;ib=na+nk:na+nb+nk-1;ic=tic+nk-1;id=tid+nk-1;iff=tif+nk-1;
iib=na+1:na+nb+nk-1;
dm=na+nbm+nc+nd+nf;
ii=[ia iib ic id iff];i=[ia ib ic id iff];
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(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*phi(i)/(lam + phi(i)'*p*phi(i));
p=(p-K*phi(i)'*p)/lam+R1;
else K=adg*phi(i);end
if adm(1)=='n', K=K/(eps+phi(i)'*phi(i));end
th=th+K*epsi;
if nb+nf>0,w=th([tib tif])'*phi([ib iff]);else w=0;end
v=[z(kcou,1);-phi(ia)]'*[1;th(ia)]-w;
epsilon=v-th([tic tid])'*phi([ic id]);
phi(ii+1)=phi(ii);
if na>0,phi(1)=-z(kcou,1);end
if nb>0,phi(na+1)=z(kcou,2);end
if nc>0,phi(na+nbm+1)=epsilon;end
if nd>0,phi(na+nbm+nc+1)=-v;end
if nf>0,phi(na+nbm+nc+nd+1)=-w;end
thm(kcou,:)=th';yhat(kcou)=yh;
end
yhat=yhat';