2963ed5ee27f477e412ae68a7725cc40a1b5a90f
[scilab.git] / 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>