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th = canstart(z,pobs,nu,dkx,auxord)
CANSTART State-space model with initial parameter estimates.
THETA = CANSTART(Z,ORDERS,NU,DKX,AUXORD)
THETA: The resulting model, parametrized according to the orders
and with initial parameter estimates calculated
from data. No model covariances are given.
Z : The output-input data [y u], with each input/output component
as a column vector.
ORDERS: The model order. Optionally this argument can be given as a
vector with as many entries as there are output channels.
The model order is then the sum of these entries. Basically,
ORDERS(k) gives the number of delays of output # k that are
used by the model, and a canonical parametrization is built
up accordingly.
NU: The number of inputs.
DKX: This is a vector defining the structure: DKX =[D,K,X]
D=1 indicates that a direct term from input to output will be
estimated, while D=0 means that a delay from input to output
is postulated.
K=1 indicates that the K-matrix is estimated, while K=0 means that
K will be fixed to zero.
X=1 indicates that the initial state is estimated, X=0 that the
initial state is set to zero.
To define an arbitrary input delay structure NK, where NK(ku) is
the delay from input number ku to any of the outputs, let
DKX=[D,K,X,NK]. NK is thus a row vector of length=no of input
channels. When NK is specified, it overrides the value of D.
Default: DKX = [0, 1, 1]
AUXORD: The auxiliary order to be used by N4SID.
THETA is just an initial estimate of the system, and could be further
improved by TH = PEM(z,THETA);
See also N4SID, PEM, THETA.
| This function calls | This function is called by |
|---|---|
function th = canstart(z,pobs,nu,dkx,auxord)
% L. Ljung 21-9-90,9-26-93
% Copyright (c) 1986-98 by The MathWorks, Inc.
% $Revision: 2.6 $ $Date: 1997/12/02 03:42:28 $
if nargin<3
disp('Usage: TH = CANSTART(Z,ORDERS,NU)')
disp(' TH = CANSTART(Z,ORDERS,NU,DKX,AUXORD)')
return
end
if nargin<5,auxord=[];end
if nargin>3,
if isstr(dkx),if strcmp(dkx,'oe'),dkx=[0,0,1];else dkx=[0,1,1];end,end
end
% The above is to accomodate the old syntax.
if nargin<4,dkx=[];end,if isempty(dkx),dkx=[0,1,1];end
if length(dkx)<2,dkx(1)=0;dkx(3)=1;end
if length(dkx)<3,dkx(3)=1;end
dkxn4=dkx;
if length(dkx)>3
nk=dkx(4:length(dkx));
if length(nk)~=nu
disp(str2mat('If you specify a delay structure in DKX,',...
'you must give the delay for each input,',...
' i.e. DKX must have length 3+no of inputs.'));
error(' ')
end
if any(nk~=fix(nk))|any(nk<0)
error(['The delays must be non-negative integers.'])
end
if any(nk==0),dkx(1)=1;else dkx(1)=0;end
dkxn4=[dkx(1:3),1-(nk==0)];
elseif dkx(1), nk=zeros(1,nu);
else nk=ones(1,nu);
end
[Ncap,nz]=size(z);
if nu==0&dkx(2)==0
error('For a time-series model, the K-matrix has to be estimated.')
end
psobs=pobs;
if any(psobs<0)
error('The order indices must be non-negative.')
end
ny=length(pobs);
if ny==1,
ny=nz-nu;
if ny>1
ind1=floor(pobs/ny);
for kc=1:ny-1
psobs(kc)=ind1;
end
psobs(ny)=pobs-sum(psobs);
end
end
if nz~=nu+ny|ny<1, error(['The number of inputs and outputs in the data vector is not'...
' consistent with the number of observability indices and the number of inputs.']),end
delayu=find(nk>1);
if ~isempty(delayu)
zt=z(max(nk):Ncap,:);
for ku=delayu(:)'
zt(:,ny+ku)=z(max(nk)-nk(ku)+1:Ncap+1-nk(ku),ny+ku);
end
z=zt;
end
[Ncap,nz]=size(z);
th = n4sid(z,sum(psobs),length(psobs),auxord,dkxn4);
if isempty(th),return,end
th = ss2th(th,psobs,dkx);
th(2,7)=24;