scilab/modules/cacsd/help/en_US/armax1.xml

   1 <?xml version="1.0" encoding="UTF-8"?>
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  13 <refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="armax1">
  14     <refnamediv>
  15         <refname>armax1</refname>
  16         <refpurpose>armax identification</refpurpose>
  17     </refnamediv>
  18     <refsynopsisdiv>
  19         <title>Calling Sequence</title>
  20         <synopsis>[arc,resid]=armax1(r,s,q,y,u [,b0f])</synopsis>
  21     </refsynopsisdiv>
  22     <refsection>
  23         <title>Arguments</title>
  24         <variablelist>
  25             <varlistentry>
  26                 <term>y</term>
  27                 <listitem>
  28                     <para>output signal</para>
  29                 </listitem>
  30             </varlistentry>
  31             <varlistentry>
  32                 <term>u</term>
  33                 <listitem>
  34                     <para>input signal</para>
  35                 </listitem>
  36             </varlistentry>
  37             <varlistentry>
  38                 <term>r,s,q</term>
  39                 <listitem>
  40                     <para>auto regression orders with r &gt;=0, s &gt;=-1.</para>
  41                 </listitem>
  42             </varlistentry>
  43             <varlistentry>
  44                 <term>b0f</term>
  45                 <listitem>
  46                     <para>optional parameter. Its default value is 0 and it
  47                         means that the coefficient b0 must be identified. if bof=1
  48                         the b0 is supposed to be zero and is not identified
  49                     </para>
  50                 </listitem>
  51             </varlistentry>
  52             <varlistentry>
  53                 <term>arc</term>
  54                 <listitem>
  55                     <para>is tlist with type "ar" and fields a,  b,  d,  ny,  nu,  sig</para>
  56                     <variablelist>
  57                         <varlistentry>
  58                             <term>a</term>
  59                             <listitem>
  60                                 <para>
  61                                     is the vector <literal>[1,a1,...,a_r]</literal>
  62                                 </para>
  63                             </listitem>
  64                         </varlistentry>
  65                         <varlistentry>
  66                             <term>b</term>
  67                             <listitem>
  68                                 <para>
  69                                     is the vector <literal>[b0,......,b_s]</literal>
  70                                 </para>
  71                             </listitem>
  72                         </varlistentry>
  73                         <varlistentry>
  74                             <term>d</term>
  75                             <listitem>
  76                                 <para>
  77                                     is the vector <literal>[1,d1,....,d_q]</literal>
  78                                 </para>
  79                             </listitem>
  80                         </varlistentry>
  81                         <varlistentry>
  82                             <term>sig</term>
  83                             <listitem>
  84                                 <para>  resid=[ sig*echap(1),....,];</para>
  85                             </listitem>
  86                         </varlistentry>
  87                     </variablelist>
  88                 </listitem>
  89             </varlistentry>
  90         </variablelist>
  91     </refsection>
  92     <refsection>
  93         <title>Description</title>
  94         <para>
  95             armax1 is used to identify the coefficients of a 1-dimensional
  96             ARX process:
  97         </para>
  98         <programlisting role=""><![CDATA[
  99 A(z^-1)y= B(z^-1)u + D(z^-1)sig*e(t)
 100 e(t) is a 1-dimensional white noise with variance 1.
 101 A(z)= 1+a1*z+...+a_r*z^r; ( r=0 => A(z)=1)
 102 B(z)= b0+b1*z+...+b_s z^s ( s=-1 => B(z)=0)
 103 D(z)= 1+d1*z+...+d_q*z^q  ( q=0 => D(z)=1)
 104  ]]></programlisting>
 105         <para>
 106             for the method, see Eykhoff in trends and progress in system
 107             identification) page 96.  with
 108         </para>
 109         <programlisting role=""><![CDATA[
 110 z(t)=[y(t-1),..,y(t-r),u(t),...,
 111       u(t-s),e(t-1),...,e(t-q)]
 112  ]]></programlisting>
 113         <para>
 114             and
 115         </para>
 116         <programlisting role=""><![CDATA[
 117 coef= [-a1,..,-ar,b0,...,b_s,d1,...,d_q]'
 118 y(t)= coef'* z(t) + sig*e(t).
 119  ]]></programlisting>
 120         <para>
 121             a sequential version of the AR estimation where e(t-i) is replaced
 122             by an estimated value is used (RLLS). With q=0 this method is exactly
 123             a sequential version of armax
 124         </para>
 125     </refsection>
 126     <refsection>
 127         <title>Important notice</title>
 128         <para>In Scilab versions up to 4.1.2 the returned value in
 129             <literal>arc.sig</literal> is the square of <literal>sig</literal>
 130             square. To be conform with the help, the display of arma models
 131             and the armax function, starting from Scilab-5.0 version the
 132             returned <literal>arc.sig</literal> is <literal>sig</literal>.
 133         </para>
 134     </refsection>
 135 </refentry>