bfb1f0e5d258c43592299973c5a2e7f5a4487065
[scilab.git] / scilab / modules / cacsd / help / en_US / armax1.xml
1 <?xml version="1.0" encoding="UTF-8"?>
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13 <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="armax1">
14     <refnamediv>
15         <refname>armax1</refname>
16         <refpurpose>armax identification</refpurpose>
17     </refnamediv>
18     <refsynopsisdiv>
19         <title>Calling Sequence</title>
20         <synopsis>[arc,resid]=armax1(r,s,q,y,u [,b0f])</synopsis>
21     </refsynopsisdiv>
22     <refsection>
23         <title>Arguments</title>
24         <variablelist>
25             <varlistentry>
26                 <term>y</term>
27                 <listitem>
28                     <para>output signal</para>
29                 </listitem>
30             </varlistentry>
31             <varlistentry>
32                 <term>u</term>
33                 <listitem>
34                     <para>input signal</para>
35                 </listitem>
36             </varlistentry>
37             <varlistentry>
38                 <term>r,s,q</term>
39                 <listitem>
40                     <para>auto regression orders with r &gt;=0, s &gt;=-1.</para>
41                 </listitem>
42             </varlistentry>
43             <varlistentry>
44                 <term>b0f</term>
45                 <listitem>
46                     <para>optional parameter. Its default value is 0 and it
47                         means that the coefficient b0 must be identified. if bof=1
48                         the b0 is supposed to be zero and is not identified
49                     </para>
50                 </listitem>
51             </varlistentry>
52             <varlistentry>
53                 <term>arc</term>
54                 <listitem>
55                     <para>is tlist with type "ar" and fields a,  b,  d,  ny,  nu,  sig</para>
56                     <variablelist>
57                         <varlistentry>
58                             <term>a</term>
59                             <listitem>
60                                 <para>
61                                     is the vector <literal>[1,a1,...,a_r]</literal>
62                                 </para>
63                             </listitem>
64                         </varlistentry>
65                         <varlistentry>
66                             <term>b</term>
67                             <listitem>
68                                 <para>
69                                     is the vector <literal>[b0,......,b_s]</literal>
70                                 </para>
71                             </listitem>
72                         </varlistentry>
73                         <varlistentry>
74                             <term>d</term>
75                             <listitem>
76                                 <para>
77                                     is the vector <literal>[1,d1,....,d_q]</literal>
78                                 </para>
79                             </listitem>
80                         </varlistentry>
81                         <varlistentry>
82                             <term>sig</term>
83                             <listitem>
84                                 <para>  resid=[ sig*echap(1),....,];</para>
85                             </listitem>
86                         </varlistentry>
87                     </variablelist>
88                 </listitem>
89             </varlistentry>
90         </variablelist>
91     </refsection>
92     <refsection>
93         <title>Description</title>
94         <para>
95             armax1 is used to identify the coefficients of a 1-dimensional 
96             ARX process:
97         </para>
98         <programlisting role=""><![CDATA[ 
99 A(z^-1)y= B(z^-1)u + D(z^-1)sig*e(t)
100 e(t) is a 1-dimensional white noise with variance 1.
101 A(z)= 1+a1*z+...+a_r*z^r; ( r=0 => A(z)=1)
102 B(z)= b0+b1*z+...+b_s z^s ( s=-1 => B(z)=0)
103 D(z)= 1+d1*z+...+d_q*z^q  ( q=0 => D(z)=1)
104  ]]></programlisting>
105         <para>
106             for the method, see Eykhoff in trends and progress in system
107             identification) page 96.  with
108         </para>
109         <programlisting role=""><![CDATA[ 
110 z(t)=[y(t-1),..,y(t-r),u(t),...,
111       u(t-s),e(t-1),...,e(t-q)] 
112  ]]></programlisting>
113         <para>
114             and
115         </para>
116         <programlisting role=""><![CDATA[ 
117 coef= [-a1,..,-ar,b0,...,b_s,d1,...,d_q]'
118 y(t)= coef'* z(t) + sig*e(t).
119  ]]></programlisting>
120         <para>
121             a sequential version of the AR estimation where e(t-i) is replaced 
122             by an estimated value is used (RLLS). With q=0 this method is exactly
123             a sequential version of armax
124         </para>
125     </refsection>
126     <refsection>
127         <title>Important notice</title>
128         <para>In Scilab versions up to 4.1.2 the returned value in
129             <literal>arc.sig</literal> is the square of <literal>sig</literal>
130             square. To be conform with the help, the display of arma models
131             and the armax function, starting from Scilab-5.0 version the
132             returned <literal>arc.sig</literal> is <literal>sig</literal>. 
133         </para>
134     </refsection>
135 </refentry>