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  • Committer: Package Import Robot
  • Author(s): Sylvestre Ledru
  • Date: 2012-08-30 14:42:38 UTC
  • mfrom: (1.4.7)
  • Revision ID: package-import@ubuntu.com-20120830144238-c1y2og7dbm7m9nig
Tags: 5.4.0-beta-3-1~exp1
* New upstream release
* Update the scirenderer dep
* Get ride of libjhdf5-java dependency

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modules/signal_processing/help/en_US/filters/wiener.xml
 
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<?xml version="1.0" encoding="UTF-8"?>
 
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<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"  version="5.0-subset Scilab" xml:lang="en" xml:id="wiener">
 
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    <refnamediv>
 
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        <refname>wiener</refname>
 
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        <refpurpose>  Wiener estimate</refpurpose>
 
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    </refnamediv>
 
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    <refsynopsisdiv>
 
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        <title>Calling Sequence</title>
 
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        <synopsis>[xs,ps,xf,pf]=wiener(y,x0,p0,f,g,h,q,r)</synopsis>
 
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    </refsynopsisdiv>
 
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    <refsection>
 
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        <title>Arguments</title>
 
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        <variablelist>
 
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            <varlistentry>
 
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                <term>f, g, h</term>
 
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                <listitem>
 
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                    <para>
 
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                        system matrices in the interval <literal>[t0,tf]</literal>
 
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                    </para>
 
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                    <variablelist>
 
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                        <varlistentry>
 
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                            <term>f</term>
 
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                            <listitem>
 
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                                <para>
 
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                                    =<literal>[f0,f1,...,ff]</literal>, and <literal>fk</literal> is a nxn matrix
 
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                                </para>
 
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                            </listitem>
 
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                        </varlistentry>
 
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                        <varlistentry>
 
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                            <term>g</term>
 
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                            <listitem>
 
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                                <para>
 
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                                    =<literal>[g0,g1,...,gf]</literal>, and <literal>gk</literal> is a nxn matrix
 
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                                </para>
 
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                            </listitem>
 
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                        </varlistentry>
 
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                        <varlistentry>
 
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                            <term>h</term>
 
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                            <listitem>
 
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                                <para>
 
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                                    =<literal>[h0,h1,...,hf]</literal>, and <literal>hk</literal> is a mxn matrix
 
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                                </para>
 
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                            </listitem>
 
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                        </varlistentry>
 
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                    </variablelist>
 
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                </listitem>
 
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            </varlistentry>
 
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            <varlistentry>
 
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                <term>q, r</term>
 
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                <listitem>
 
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                    <para>covariance matrices of dynamics and observation noise</para>
 
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                    <variablelist>
 
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                        <varlistentry>
 
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                            <term>q</term>
 
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                            <listitem>
 
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                                <para>
 
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                                    =<literal>[q0,q1,...,qf]</literal>, and <literal>qk</literal> is a nxn matrix
 
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                                </para>
 
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                            </listitem>
 
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                        </varlistentry>
 
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                        <varlistentry>
 
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                            <term>r</term>
 
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                            <listitem>
 
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                                <para>
 
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                                    =<literal>[r0,r1,...,rf]</literal>, and <literal>gk</literal> is a mxm matrix
 
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                                </para>
 
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                            </listitem>
 
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                        </varlistentry>
 
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                    </variablelist>
 
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                </listitem>
 
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            </varlistentry>
 
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            <varlistentry>
 
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                <term>x0, p0</term>
 
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                <listitem>
 
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                    <para>initial state estimate and error variance</para>
 
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                </listitem>
 
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            </varlistentry>
 
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            <varlistentry>
 
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                <term>y</term>
 
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                <listitem>
 
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                    <para>
 
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                        observations in the interval <literal>[t0,tf]</literal>. <literal>y=[y0,y1,...,yf]</literal>, and <literal>yk</literal> is a column m-vector
 
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                    </para>
 
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                </listitem>
 
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            </varlistentry>
 
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            <varlistentry>
 
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                <term>xs</term>
 
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                <listitem>
 
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                    <para>
 
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                        Smoothed state estimate <literal>xs= [xs0,xs1,...,xsf]</literal>, and <literal>xsk</literal> is a column n-vector
 
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                    </para>
 
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                </listitem>
 
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            </varlistentry>
 
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            <varlistentry>
 
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                <term>ps</term>
 
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                <listitem>
 
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                    <para>
 
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                        Error covariance of smoothed estimate <literal>ps=[p0,p1,...,pf]</literal>, and <literal>pk</literal> is a nxn matrix
 
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                    </para>
 
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                </listitem>
 
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            </varlistentry>
 
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            <varlistentry>
 
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                <term>xf</term>
 
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                <listitem>
 
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                    <para>
 
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                        Filtered state estimate <literal>xf= [xf0,xf1,...,xff]</literal>, and <literal>xfk</literal> is a column n-vector
 
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                    </para>
 
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                </listitem>
 
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            </varlistentry>
 
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            <varlistentry>
 
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                <term>pf</term>
 
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                <listitem>
 
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                    <para>
 
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                        Error covariance of filtered estimate <literal>pf=[p0,p1,...,pf]</literal>, and <literal>pk</literal> is a nxn matrix
 
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                    </para>
 
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                </listitem>
 
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            </varlistentry>
 
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        </variablelist>
 
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    </refsection>
 
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    <refsection>
 
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        <title>Description</title>
 
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        <para>
 
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            function which gives the Wiener estimate using
 
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            the forward-backward Kalman filter formulation
 
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        </para>
 
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    </refsection>
 
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    <refsection>
 
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        <title>Sample</title>
 
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        <scilab:image>
 
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            m0=[10 10]';
 
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            p0=[100 0;0 100];
 
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            f2=[1.1 50.1;0 0.8];
 
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            g=[1 0;0 1];
 
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            h=[1 0;0 1];
 
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            [hi,hj]=size(h);
 
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            q=[.01 0;0 0.01];
 
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            r=20*eye(2,2);
 
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            rand("seed",66);
 
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            rand("normal");
 
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            p0c=chol(p0);
 
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            x0=m0+p0c'*rand(ones(m0));
 
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            y=h*x0+chol(r)'*rand(ones(1:hi))';
 
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            yt=y;
 
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            x=x0;
 
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            ft=[f2];
 
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            gt=[g];
 
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            ht=[h];
 
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            qt=[q];
 
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            rt=[r];
 
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            n=10;
 
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            for k=1:n
 
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            [x1,y]=system(x0,f2,g,h,q,r);
 
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            x=[x x1];
 
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            yt=[yt y];
 
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            x0=x1;
 
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            ft=[ft f2];
 
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            gt=[gt g];
 
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            ht=[ht h];
 
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            qt=[qt q];
 
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            rt=[rt r];
 
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            end
 
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            [xs,ps,xf,pf]=wiener(yt,m0,p0,ft,gt,ht,qt,rt);
 
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            a=min([x(1,:)-2*sqrt(ps(1,1:2:2*(n+1))),xf(1,:),xs(1,:)]);
 
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            b=max([x(1,:)+2*sqrt(ps(1,1:2:2*(n+1))),xf(1,:),xs(1,:)]);
 
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            c=min([x(2,:)-2*sqrt(ps(2,2:2:2*(n+1))),xf(2,:),xs(2,:)]);
 
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            d=max([x(2,:)+2*sqrt(ps(2,2:2:2*(n+1))),xf(2,:),xs(2,:)]);
 
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            xmargin=max([abs(a),abs(b)]);
 
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            ymargin=max([abs(c),abs(d)]);
 
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            a=-0.1*xmargin+a;
 
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            b=.1*xmargin+b;
 
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            c=-0.1*ymargin+c;
 
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            d=.1*ymargin+d;
 
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            scf();
 
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            plot([a a b],[d c c]);
 
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            plot2d(x(1,:)',x(2,:)',[2],"000")
 
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            plot2d(xf(1,:)',xf(2,:)',[2],"000")
 
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            plot2d(xs(1,:)',xs(2,:)',[2],"000")
 
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            plot2d(xs(1,:)',xs(2,:)',[-2],"000")
 
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            plot2d(xf(1,:)',xf(2,:)',[-3],"000")
 
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            plot2d(x(1,:)',x(2,:)',[-4],"000")
 
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        </scilab:image>
 
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    </refsection>
 
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    <refsection>
 
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        <title>Examples</title>
 
185
        <programlisting role="example"><![CDATA[ 
 
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// initialize state statistics (mean and er. variance)
 
187
m0=[10 10]';
 
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p0=[100 0;0 100];
 
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// create system
 
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f2=[1.1 50.1;0 0.8];
 
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g=[1 0;0 1];
 
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h=[1 0;0 1];
 
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[hi,hj]=size(h);
 
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// noise statistics
 
195
q=[.01 0;0 0.01];
 
196
r=20*eye(2,2);
 
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// initialize system process
 
198
rand("seed",66);
 
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rand("normal");
 
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p0c=chol(p0);
 
201
x0=m0+p0c'*rand(ones(m0));
 
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y=h*x0+chol(r)'*rand(ones(1:hi))';
 
203
yt=y;
 
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// initialize plotted variables
 
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x=x0;
 
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// loop
 
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ft=[f2];
 
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gt=[g];
 
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ht=[h];
 
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qt=[q];
 
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rt=[r];
 
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n=10;
 
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for k=1:n
 
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    // generate the state and observation 
 
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    // at time k (i.e. xk and yk)
 
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    [x1,y]=system(x0,f2,g,h,q,r);
 
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    x=[x x1];
 
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    yt=[yt y];
 
219
    x0=x1;
 
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    ft=[ft f2];
 
221
    gt=[gt g];
 
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    ht=[ht h];
 
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    qt=[qt q];
 
224
    rt=[rt r];
 
225
end
 
226
// get the wiener filter estimate
 
227
[xs,ps,xf,pf]=wiener(yt,m0,p0,ft,gt,ht,qt,rt);
 
228
// plot result
 
229
a=min([x(1,:)-2*sqrt(ps(1,1:2:2*(n+1))),xf(1,:),xs(1,:)]);
 
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b=max([x(1,:)+2*sqrt(ps(1,1:2:2*(n+1))),xf(1,:),xs(1,:)]);
 
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c=min([x(2,:)-2*sqrt(ps(2,2:2:2*(n+1))),xf(2,:),xs(2,:)]);
 
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d=max([x(2,:)+2*sqrt(ps(2,2:2:2*(n+1))),xf(2,:),xs(2,:)]);
 
233
xmargin=max([abs(a),abs(b)]);
 
234
ymargin=max([abs(c),abs(d)]);
 
235
a=-0.1*xmargin+a;
 
236
b=.1*xmargin+b;
 
237
c=-0.1*ymargin+c;
 
238
d=.1*ymargin+d;
 
239
// plot frame, real state (x), and estimates (xf, and xs)
 
240
scf();
 
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plot([a a b],[d c c]);
 
242
plot2d(x(1,:)',x(2,:)',[2],"000")
 
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plot2d(xf(1,:)',xf(2,:)',[2],"000")
 
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plot2d(xs(1,:)',xs(2,:)',[2],"000")
 
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// mark data points (* for real data, o for estimates)
 
246
plot2d(xs(1,:)',xs(2,:)',[-2],"000")
 
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plot2d(xf(1,:)',xf(2,:)',[-3],"000")
 
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plot2d(x(1,:)',x(2,:)',[-4],"000")
 
249
 ]]></programlisting>
 
250
    </refsection>
 
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</refentry>