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<!DOCTYPE MAN SYSTEM "../../manrev.dtd">
<MAN>
  <LANGUAGE>eng</LANGUAGE>
  <TITLE>armax1</TITLE>
  <TYPE>Scilab Function</TYPE>
  <DATE>April 1993</DATE>
  <SHORT_DESCRIPTION name="armax1"> armax identification</SHORT_DESCRIPTION>
  <CALLING_SEQUENCE>
    <CALLING_SEQUENCE_ITEM>[arc,resid]=armax1(r,s,q,y,u [,b0f])  </CALLING_SEQUENCE_ITEM>
  </CALLING_SEQUENCE>
  <PARAM>
    <PARAM_INDENT>
      <PARAM_ITEM>
        <PARAM_NAME>y</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>: output signal</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
      <PARAM_ITEM>
        <PARAM_NAME>u</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>: input signal</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
      <PARAM_ITEM>
        <PARAM_NAME>r,s,q</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>: auto regression orders with r &gt;=0, s &gt;=-1.</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
      <PARAM_ITEM>
        <PARAM_NAME>b0f</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>: 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</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
      <PARAM_ITEM>
        <PARAM_NAME>arc</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>: is tlist with type &quot;ar&quot; and fields a,  b,  d,  ny,  nu,  sig</SP>
          <PARAM_INDENT>
            <PARAM_ITEM>
              <PARAM_NAME>a</PARAM_NAME>
              <PARAM_DESCRIPTION>
                <SP>: is the vector [1,a1,...,a_r]</SP>
              </PARAM_DESCRIPTION>
            </PARAM_ITEM>
            <PARAM_ITEM>
              <PARAM_NAME>b</PARAM_NAME>
              <PARAM_DESCRIPTION>
                <SP>: is the vector [b0,......,b_s]</SP>
              </PARAM_DESCRIPTION>
            </PARAM_ITEM>
            <PARAM_ITEM>
              <PARAM_NAME>d</PARAM_NAME>
              <PARAM_DESCRIPTION>
                <SP>: is the vector [1,d1,....,d_q]</SP>
              </PARAM_DESCRIPTION>
            </PARAM_ITEM>
            <PARAM_ITEM>
              <PARAM_NAME>sig</PARAM_NAME>
              <PARAM_DESCRIPTION>
                <SP>:   resid=[ sig*echap(1),....,];</SP>
              </PARAM_DESCRIPTION>
            </PARAM_ITEM>
          </PARAM_INDENT>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
    </PARAM_INDENT>
  </PARAM>
  <DESCRIPTION>
    <P>
    armax1 is used to identify the coefficients of a 1-dimensional 
    ARX process:</P>
    <VERBATIM>
<![CDATA[
   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)
   ]]>
    </VERBATIM>
    <P>
    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).</P>
    <P>
    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</P>
  </DESCRIPTION>
  <AUTHOR>J.-Ph.C; ;   </AUTHOR>
</MAN>
