armax1(1)

NAME
armax1 - armax identification

CALING SEQUENCE
[a,b,d,sig,resid]=armax1(r,s,q,y,u,[b0f])

PARAMETERS

y   : output signal

u   : input signal

r,s,q
    : autoregression orders with r >=0, 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

a   : is the vector [1,a1,...,a_r]

b   : is the vector [b0,......,b_s]

d   : is the vector [1,d1,....,d_q]

sig : resid=[ sig*echap(1),....,];

DESCRIPTION
armax1 is used to identify the coefficients of a 1-dimensional ARX process:
   A(z^-1)y= B(z^-1)u + D(z^-1)sig*e(t)
   e(t) is a 1-dimensional white noise with variance 1.
   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)
   D(z)= 1+d1*z+...+d_q*z^q  ( q=0 => D(z)=1)
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),e(t-1),...,e(t-q)] and
        coef= [-a1,..,-ar,b0,...,b_s,d1,...,d_q]'
        y(t)= coef'* z(t) + sig*e(t). a sequential version of the AR estimation where e(t-i) is replaced by an estimated value is used (RLLS). With q=0 this method is exactly a sequentiel version of armax

AUTHOR
J.-Ph.C