4c7f74b266282be02cc51b1e1ad26d7b7d5b13ac
[scilab.git] / 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>