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armax(3) Scilab Function armax(3)
NAME
armax - armax identification
CALLING SEQUENCE
[arc,la,lb,sig,resid]=armax(r,s,y,u,[b0f,prf])
PARAMETERS
y : output process y(ny,n); ( ny: dimension of y , n : sample
size)
u : input process u(nu,n); ( nu: dimension of u , n : sample
size)
r and s : auto-regression orders r >=0 et s >=-1
b0f : optional parameter. Its default value is 0 and it means
that the coefficient b0 must be identified. if bof=1 the b0
is supposed to be zero and is not identified
prf : optional parameter for display control. If prf =1, the
default value, a display of the identified Arma is given.
arc : a Scilab arma object (see armac)
la : is the list(a,a+eta,a-eta) ( la = a in dimension 1) ;
where eta is the estimated standard deviation. ,
a=[Id,a1,a2,...,ar] where each ai is a matrix of size
(ny,ny)
lb : is the list(b,b+etb,b-etb) (lb =b in dimension 1) ; where
etb is the estimated standard deviation. b=[b0,.....,b_s]
where each bi is a matrix of size (nu,nu)
sig : is the estimated standard deviation of the noise and
resid=[ sig*e(t0),....] (
DESCRIPTION
armax is used to identify the coefficients of a n-dimensional ARX process
A(z^-1)y= B(z^-1)u + sig*e(t)
where e(t) is a n-dimensional white noise with variance I. sig an nxn
matrix and A(z) and B(z):
A(z) = 1+a1*z+...+a_r*z^r; ( r=0 => A(z)=1)
B(z) = b0+b1*z+...+b_s z^s ( s=-1 => B(z)=0)
for the method see Eykhoff in trends and progress in system identification,
page 96. with
z(t)=[y(t-1),..,y(t-r),u(t),...,u(t-s)] and
coef= [-a1,..,-ar,b0,...,b_s] we can write y(t)= coef* z(t) + sig*e(t) and
the algorithm minimises sum_{t=1}^N ( [y(t)- coef'z(t)]^2) where
t0=maxi(maxi(r,s)+1,1))).
EXAMPLE
[arc,a,b,sig,resid]=armax(); // will gives an example in dimension 1
AUTHOR
J-Ph. Chancelier.
SEE ALSO
imrep2ss, time_id, arl2, armax, frep2tf
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