scilab/modules/signal_processing/help/en_US/filters/sskf.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" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="sskf">
   3     <refnamediv>
   4         <refname>sskf</refname>
   5         <refpurpose>steady-state Kalman filter</refpurpose>
   6     </refnamediv>
   7     <refsynopsisdiv>
   8         <title>Calling Sequence</title>
   9         <synopsis>[xe,pe]=sskf(y,f,h,q,r,x0)</synopsis>
  10     </refsynopsisdiv>
  11     <refsection>
  12         <title>Arguments</title>
  13         <variablelist>
  14             <varlistentry>
  15                 <term>y</term>
  16                 <listitem>
  17                     <para>
  18                         data in form <literal>[y0,y1,...,yn]</literal>, <literal>yk</literal> a column vector
  19                     </para>
  20                 </listitem>
  21             </varlistentry>
  22             <varlistentry>
  23                 <term>f</term>
  24                 <listitem>
  25                     <para>system matrix dim(NxN)</para>
  26                 </listitem>
  27             </varlistentry>
  28             <varlistentry>
  29                 <term>h</term>
  30                 <listitem>
  31                     <para>observations matrix dim(MxN)</para>
  32                 </listitem>
  33             </varlistentry>
  34             <varlistentry>
  35                 <term>q</term>
  36                 <listitem>
  37                     <para>dynamics noise matrix dim(NxN)</para>
  38                 </listitem>
  39             </varlistentry>
  40             <varlistentry>
  41                 <term>r</term>
  42                 <listitem>
  43                     <para>observations noise matrix dim(MxM)</para>
  44                 </listitem>
  45             </varlistentry>
  46             <varlistentry>
  47                 <term>x0</term>
  48                 <listitem>
  49                     <para>initial state estimate</para>
  50                 </listitem>
  51             </varlistentry>
  52             <varlistentry>
  53                 <term>xe</term>
  54                 <listitem>
  55                     <para>estimated state</para>
  56                 </listitem>
  57             </varlistentry>
  58             <varlistentry>
  59                 <term>pe</term>
  60                 <listitem>
  61                     <para>steady-state error covariance</para>
  62                 </listitem>
  63             </varlistentry>
  64         </variablelist>
  65     </refsection>
  66     <refsection>
  67         <title>Description</title>
  68         <para>
  69             steady-state Kalman filter
  70         </para>
  71     </refsection>
  72     <refsection>
  73         <title>Examples</title>
  74         <programlisting role="example"><![CDATA[
  75 rand("seed",5);
  76 rand("normal");
  77 q=[.03 0.01;.01 0.03];
  78 u=rand(2,11);
  79 f=[1.1 0.1;0 0.8];
  80 g=(chol(q))';
  81 m0=[10 10]';
  82 p0=[2 0;0 2];
  83 x0=m0+(chol(p0))'*rand(2,1);
  84 x=ltitr(f,g,u,x0);
  85 r=[2 0;0 2];
  86 v=(chol(r))'*rand(2,11);
  87 y=x+v;
  88 h=eye(2,2);
  89 [xe]=sskf(y,f,h,q,r,m0)
  90  ]]></programlisting>
  91     </refsection>
  92 </refentry>