scilab/modules/signal_processing/help/en_US/wiener.xml

   1 <?xml version="1.0" encoding="UTF-8"?>
   2 <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" version="5.0-subset Scilab" xml:lang="en" xml:id="wiener">
   3   <refnamediv>
   4     <refname>wiener</refname>
   5     <refpurpose>  Wiener estimate</refpurpose>
   6   </refnamediv>
   7   <refsynopsisdiv>
   8     <title>Calling Sequence</title>
   9     <synopsis>[xs,ps,xf,pf]=wiener(y,x0,p0,f,g,h,q,r)</synopsis>
  10   </refsynopsisdiv>
  11   <refsection>
  12     <title>Arguments</title>
  13     <variablelist>
  14       <varlistentry>
  15         <term>f, g, h</term>
  16         <listitem>
  17           <para>
  18             system matrices in the interval <literal>[t0,tf]</literal>
  19           </para>
  20           <variablelist>
  21             <varlistentry>
  22               <term>f</term>
  23               <listitem>
  24                 <para>
  25                   =<literal>[f0,f1,...,ff]</literal>, and <literal>fk</literal> is a nxn matrix
  26                 </para>
  27               </listitem>
  28             </varlistentry>
  29             <varlistentry>
  30               <term>g</term>
  31               <listitem>
  32                 <para>
  33                   =<literal>[g0,g1,...,gf]</literal>, and <literal>gk</literal> is a nxn matrix
  34                 </para>
  35               </listitem>
  36             </varlistentry>
  37             <varlistentry>
  38               <term>h</term>
  39               <listitem>
  40                 <para>
  41                   =<literal>[h0,h1,...,hf]</literal>, and <literal>hk</literal> is a mxn matrix
  42                 </para>
  43               </listitem>
  44             </varlistentry>
  45           </variablelist>
  46         </listitem>
  47       </varlistentry>
  48       <varlistentry>
  49         <term>q, r</term>
  50         <listitem>
  51           <para>covariance matrices of dynamics and observation noise</para>
  52           <variablelist>
  53             <varlistentry>
  54               <term>q</term>
  55               <listitem>
  56                 <para>
  57                   =<literal>[q0,q1,...,qf]</literal>, and <literal>qk</literal> is a nxn matrix
  58                 </para>
  59               </listitem>
  60             </varlistentry>
  61             <varlistentry>
  62               <term>r</term>
  63               <listitem>
  64                 <para>
  65                   =<literal>[r0,r1,...,rf]</literal>, and <literal>gk</literal> is a mxm matrix
  66                 </para>
  67               </listitem>
  68             </varlistentry>
  69           </variablelist>
  70         </listitem>
  71       </varlistentry>
  72       <varlistentry>
  73         <term>x0, p0</term>
  74         <listitem>
  75           <para>initial state estimate and error variance</para>
  76         </listitem>
  77       </varlistentry>
  78       <varlistentry>
  79         <term>y</term>
  80         <listitem>
  81           <para>
  82             observations in the interval <literal>[t0,tf]</literal>. <literal>y=[y0,y1,...,yf]</literal>, and <literal>yk</literal> is a column m-vector
  83           </para>
  84         </listitem>
  85       </varlistentry>
  86       <varlistentry>
  87         <term>xs</term>
  88         <listitem>
  89           <para>
  90             Smoothed state estimate <literal>xs= [xs0,xs1,...,xsf]</literal>, and <literal>xsk</literal> is a column n-vector
  91           </para>
  92         </listitem>
  93       </varlistentry>
  94       <varlistentry>
  95         <term>ps</term>
  96         <listitem>
  97           <para>
  98             Error covariance of smoothed estimate <literal>ps=[p0,p1,...,pf]</literal>, and <literal>pk</literal> is a nxn matrix
  99           </para>
 100         </listitem>
 101       </varlistentry>
 102       <varlistentry>
 103         <term>xf</term>
 104         <listitem>
 105           <para>
 106             Filtered state estimate <literal>xf= [xf0,xf1,...,xff]</literal>, and <literal>xfk</literal> is a column n-vector
 107           </para>
 108         </listitem>
 109       </varlistentry>
 110       <varlistentry>
 111         <term>pf</term>
 112         <listitem>
 113           <para>
 114             Error covariance of filtered estimate <literal>pf=[p0,p1,...,pf]</literal>, and <literal>pk</literal> is a nxn matrix
 115           </para>
 116         </listitem>
 117       </varlistentry>
 118     </variablelist>
 119   </refsection>
 120   <refsection>
 121     <title>Description</title>
 122     <para>
 123       function which gives the Wiener estimate using
 124       the forward-backward Kalman filter formulation
 125     </para>
 126   </refsection>
 127 </refentry>