armax1
======

armax identification



Calling Sequence
~~~~~~~~~~~~~~~~


::

    [arc,resid]=armax1(r,s,q,y,u [,b0f])




Arguments
~~~~~~~~~

:y output signal
: :u input signal
: :r,s,q auto regression 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
: :arc is tlist with type "ar" and fields a, b, d, ny, nu, sig
    :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
sequential version of armax



Important notice
~~~~~~~~~~~~~~~~

In Scilab versions up to 4.1.2 the returned value in `arc.sig` is the
square of `sig` square. To be conform with the help, the display of
arma models and the armax function, starting from Scilab-5.0 version
the returned `arc.sig` is `sig`.