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<!DOCTYPE MAN SYSTEM "../../manrev.dtd">
<MAN>
  <LANGUAGE>eng</LANGUAGE>
  <TITLE>faurre</TITLE>
  <TYPE>Scilab Function</TYPE>
  <DATE>April 1993</DATE>
  <SHORT_DESCRIPTION name="faurre"> filter computation by simple Faurre algorithm</SHORT_DESCRIPTION>
  <CALLING_SEQUENCE>
    <CALLING_SEQUENCE_ITEM>[P,R,T]=faurre(n,H,F,G,R0)  </CALLING_SEQUENCE_ITEM>
  </CALLING_SEQUENCE>
  <PARAM>
    <PARAM_INDENT>
      <PARAM_ITEM>
        <PARAM_NAME>n</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>: number of iterations.</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
      <PARAM_ITEM>
        <PARAM_NAME>H, F, G</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>: estimated triple from the covariance sequence of <VERB>y</VERB>.</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
      <PARAM_ITEM>
        <PARAM_NAME>R0</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>: E(yk*yk')</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
      <PARAM_ITEM>
        <PARAM_NAME>P</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>: solution of the Riccati equation after n iterations.</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
      <PARAM_ITEM>
        <PARAM_NAME>R, T</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>: gain matrix of the filter.</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
    </PARAM_INDENT>
  </PARAM>
  <DESCRIPTION>
    <P>
    This function computes iteratively the minimal solution of the algebraic
    Riccati equation and gives the matrices <VERB>R</VERB> and <VERB>T</VERB> of the 
    filter model.
    The algorithm tries to compute the solution P as the growing limit of a
    sequence of matrices Pn such that</P>
    <VERBATIM>
<![CDATA[
                                     -1
Pn+1=F*Pn*F'+(G-F*Pn*h')*(R0-H*Pn*H')  *(G'-H*Pn*F')
       -1
P0=G*R0 *G'
   ]]>
    </VERBATIM>
    <P>
    Note that this method may not converge,especially when F has poles
    near the unit circle. Use preferably the srfaur function.</P>
  </DESCRIPTION>
  <SEE_ALSO>
    <SEE_ALSO_ITEM>
      <LINK>srfaur</LINK>
    </SEE_ALSO_ITEM>
    <SEE_ALSO_ITEM>
      <LINK>lindquist</LINK>
    </SEE_ALSO_ITEM>
    <SEE_ALSO_ITEM>
      <LINK>phc</LINK>
    </SEE_ALSO_ITEM>
  </SEE_ALSO>
  <AUTHOR>G. Le V.  </AUTHOR>
</MAN>
