armax(1)

NAME
armax - armax identification

CALLING SEQUENCE
[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.

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 metho 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 minimizes sum_{t=1}^N ( [y(t)- coef'z(t)]^2) where t0=maxi(maxi(r,s)+1,1))).

EXAMPLE
[a,b,sig,resid]=armax(); will gives an example in dimension 1

AUTHOR
J-Ph.C.