.TH armax 3 "April 1993" "Scilab Group" "Scilab Function"
.so man1/sci.an
.SH NAME
armax - armax identification 
.SH CALLING SEQUENCE
.nf
[la,lb,sig,resid]=armax(r,s,y,u,[b0f,prf])
.fi 
.SH PARAMETERS
.TP 15
y 
: output process  y(ny,n); ( ny: dimension of y , n : sample size) 
.TP
u 
: input process   u(nu,n); ( nu: dimension of u , n : sample size) 
.TP
r and s 
: auto-regression orders r >=0 et s >=-1
.TP
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 
.TP
prf 
: optional parameter for display control. If prf =1, the default value, 
a display of the identified Arma is given.
.TP
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)
.TP
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)
.TP
sig
: is the estimated standard deviation of the noise and resid=[ sig*e(t0),....] ( 
.SH DESCRIPTION
armax is used to identify the coefficients of a n-dimensional 
ARX process
.nf 
   A(z^-1)y= B(z^-1)u + sig*e(t)
.fi
where e(t) is a n-dimensional white noise with variance I.
sig  an nxn matrix and A(z) and B(z):
.nf
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)
.fi
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))).
.SH EXAMPLE
.nf 
[a,b,sig,resid]=armax(); // will gives an example in dimension 1
.fi
.SH AUTHOR 
J-Ph. Chancelier.
.SH SEE ALSO
imrep2ss , time_id, arl2 , armax, frep2tf