* Bug #4504 fixed - Function sskf did not work with two outputs (+ help page updated).
[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>
10             xe = sskf(y,f,h,q,r,x0)
11             [xe, pe]=sskf(y,f,h,q,r,x0)
12         </synopsis>
13     </refsynopsisdiv>
14     <refsection>
15         <title>Arguments</title>
16         <variablelist>
17             <varlistentry>
18                 <term>y</term>
19                 <listitem>
20                     <para>
21                         data in form <literal>[y0,y1,...,yn]</literal>, <literal>yk</literal> a column vector
22                     </para>
23                 </listitem>
24             </varlistentry>
25             <varlistentry>
26                 <term>f</term>
27                 <listitem>
28                     <para>system matrix dim(NxN)</para>
29                 </listitem>
30             </varlistentry>
31             <varlistentry>
32                 <term>h</term>
33                 <listitem>
34                     <para>observations matrix dim(MxN)</para>
35                 </listitem>
36             </varlistentry>
37             <varlistentry>
38                 <term>q</term>
39                 <listitem>
40                     <para>dynamics noise matrix dim(NxN)</para>
41                 </listitem>
42             </varlistentry>
43             <varlistentry>
44                 <term>r</term>
45                 <listitem>
46                     <para>observations noise matrix dim(MxM)</para>
47                 </listitem>
48             </varlistentry>
49             <varlistentry>
50                 <term>x0</term>
51                 <listitem>
52                     <para>initial state estimate</para>
53                 </listitem>
54             </varlistentry>
55             <varlistentry>
56                 <term>xe</term>
57                 <listitem>
58                     <para>estimated state</para>
59                 </listitem>
60             </varlistentry>
61             <varlistentry>
62                 <term>pe</term>
63                 <listitem>
64                     <para>steady-state error covariance</para>
65                 </listitem>
66             </varlistentry>
67         </variablelist>
68     </refsection>
69     <refsection>
70         <title>Description</title>
71         <para>
72             steady-state Kalman filter
73         </para>
74     </refsection>
75     <refsection>
76         <title>Examples</title>
77         <programlisting role="example"><![CDATA[ 
78 rand("seed",5);
79 rand("normal");
80 q=[.03 0.01;.01 0.03];
81 u=rand(2,11);
82 f=[1.1 0.1;0 0.8];
83 g=(chol(q))';
84 m0=[10 10]';
85 p0=[2 0;0 2];
86 x0=m0+(chol(p0))'*rand(2,1);
87 x=ltitr(f,g,u,x0);
88 r=[2 0;0 2];
89 v=(chol(r))'*rand(2,11);
90 y=x+v;
91 h=eye(2,2);
92 [xe pe]=sskf(y,f,h,q,r,m0)
93  ]]></programlisting>
94     </refsection>
95 </refentry>