hp48g(x) discrete kalman filter simulator.htm

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src="HP48G(X) Discrete Kalman Filter Simulator.files/img37.gif" width=13 
align=bottom> matrix is: 
<P><IMG height=86 alt=displaymath275 
src="HP48G(X) Discrete Kalman Filter Simulator.files/img38.gif" width=296 
align=bottom> 
<P>
<P>The <IMG height=15 alt=tex2html_wrap145 
src="HP48G(X) Discrete Kalman Filter Simulator.files/img30.gif" width=13 
align=bottom> vector is: 
<P><IMG height=86 alt=displaymath276 
src="HP48G(X) Discrete Kalman Filter Simulator.files/img39.gif" width=268 
align=bottom> 
<P>
<P>The <IMG height=13 alt=tex2html_wrap153 
src="HP48G(X) Discrete Kalman Filter Simulator.files/img40.gif" width=16 
align=bottom> vector is: 
<P><IMG height=48 alt=displaymath277 
src="HP48G(X) Discrete Kalman Filter Simulator.files/img41.gif" width=280 
align=bottom> 
<P>
<P>The <IMG height=14 alt=tex2html_wrap120 
src="HP48G(X) Discrete Kalman Filter Simulator.files/img14.gif" width=19 
align=bottom> matrix is: 
<P><IMG height=86 alt=displaymath278 
src="HP48G(X) Discrete Kalman Filter Simulator.files/img42.gif" width=281 
align=bottom> 
<P>
<P>The measurement error covariance <IMG height=14 alt=tex2html_wrap155 
src="HP48G(X) Discrete Kalman Filter Simulator.files/img43.gif" width=13 
align=bottom> is: 
<P><IMG height=48 alt=displaymath279 
src="HP48G(X) Discrete Kalman Filter Simulator.files/img44.gif" width=275 
align=bottom> 
<P>
<P>And we will assume <IMG height=17 alt=tex2html_wrap156 
src="HP48G(X) Discrete Kalman Filter Simulator.files/img45.gif" width=60 
align=bottom> and <IMG height=11 alt=tex2html_wrap157 
src="HP48G(X) Discrete Kalman Filter Simulator.files/img46.gif" width=16 
align=bottom> to be: 
<P><IMG height=86 alt=displaymath280 
src="HP48G(X) Discrete Kalman Filter Simulator.files/img47.gif" width=379 
align=bottom> 
<P>
<P>
<P><IMG height=20 alt=tex2html_wrap158 
src="HP48G(X) Discrete Kalman Filter Simulator.files/img48.gif" width=13 
align=bottom> The first step is to edit the " <IMG height=13 
alt=tex2html_wrap159 
src="HP48G(X) Discrete Kalman Filter Simulator.files/img49.gif" width=55 
align=bottom> " program and make the modefications shown below: <B>
<P>?[[ 0 1 ] [ -4 -4 ]] 'F' STO [[ 0 ] [ 1 ]] 'G' STO [[ 1 1 ]] 'H' STO [[ 1 ]] 
'W' STO .2 'T' STO [[ 0 ] [ 0 ]] [[ .2 ]] 'R' STO 'XHM' STO [[ .03125 0 ] [ 0 
.125 ]] 'PM' STO [[ 0 ] [ 0 ]] 'X' STO 10 'KMAX' STO 1 'EL' STO? </B>
<P>Here <B>'EL' </B>is the state to be plotted, and <B>'KMAX'</B> is the maximum 
range to be simulated. 
<P>
<P><IMG height=13 alt=tex2html_wrap160 
src="HP48G(X) Discrete Kalman Filter Simulator.files/img50.gif" width=7 
align=bottom> ) Run this program ( <IMG height=13 alt=tex2html_wrap159 
src="HP48G(X) Discrete Kalman Filter Simulator.files/img49.gif" width=55 
align=bottom> ) to store the values just edited. 
<P><IMG height=13 alt=tex2html_wrap162 
src="HP48G(X) Discrete Kalman Filter Simulator.files/img51.gif" width=8 
align=bottom> ) Run <IMG height=18 alt=tex2html_wrap133 
src="HP48G(X) Discrete Kalman Filter Simulator.files/img21.gif" width=37 
align=bottom> to calculate <IMG height=17 alt=tex2html_wrap164 
src="HP48G(X) Discrete Kalman Filter Simulator.files/img52.gif" width=10 
align=bottom> and <IMG height=18 alt=tex2html_wrap134 
src="HP48G(X) Discrete Kalman Filter Simulator.files/img22.gif" width=13 
align=bottom> 
<P><IMG height=14 alt=tex2html_wrap166 
src="HP48G(X) Discrete Kalman Filter Simulator.files/img53.gif" width=8 
align=bottom> ) Run <IMG height=15 alt=tex2html_wrap135 
src="HP48G(X) Discrete Kalman Filter Simulator.files/img23.gif" width=63 
align=bottom> to generate the state white sequence <IMG height=9 
alt=tex2html_wrap168 
src="HP48G(X) Discrete Kalman Filter Simulator.files/img54.gif" width=13 
align=bottom> 
<P><IMG height=13 alt=tex2html_wrap169 
src="HP48G(X) Discrete Kalman Filter Simulator.files/img55.gif" width=9 
align=bottom> ) Run <IMG height=15 alt=tex2html_wrap137 
src="HP48G(X) Discrete Kalman Filter Simulator.files/img24.gif" width=66 
align=bottom> to generate the output white sequence <IMG height=9 
alt=tex2html_wrap171 
src="HP48G(X) Discrete Kalman Filter Simulator.files/img56.gif" width=9 
align=bottom> 
<P><IMG height=14 alt=tex2html_wrap172 
src="HP48G(X) Discrete Kalman Filter Simulator.files/img57.gif" width=8 
align=bottom> ) Run <IMG height=15 alt=tex2html_wrap139 
src="HP48G(X) Discrete Kalman Filter Simulator.files/img25.gif" width=65 
align=bottom> to do the simulation (it will take some time). 
<P><IMG height=14 alt=tex2html_wrap174 
src="HP48G(X) Discrete Kalman Filter Simulator.files/img58.gif" width=8 
align=bottom> ) And then <IMG height=17 alt=tex2html_wrap175 
src="HP48G(X) Discrete Kalman Filter Simulator.files/img59.gif" width=55 
align=bottom> , and <IMG height=9 alt=tex2html_wrap147 
src="HP48G(X) Discrete Kalman Filter Simulator.files/img32.gif" width=8 
align=bottom> can be ploted using <IMG height=18 alt=tex2html_wrap177 
src="HP48G(X) Discrete Kalman Filter Simulator.files/img60.gif" width=200 
align=bottom> , and <IMG height=15 alt=tex2html_wrap146 
src="HP48G(X) Discrete Kalman Filter Simulator.files/img31.gif" width=51 
align=bottom> . 
<P><IMG height=14 alt=tex2html_wrap179 
src="HP48G(X) Discrete Kalman Filter Simulator.files/img61.gif" width=8 
align=bottom> ) Now go into the picture mode to see the results. 
<P><B>NOTES:</B> The programs needed compose a total of 10K of memory, but once 
the databases are created, this number grows substantially. Run <IMG height=15 
alt=tex2html_wrap180 
src="HP48G(X) Discrete Kalman Filter Simulator.files/img62.gif" width=73 
align=bottom> to clear the databases. The larger the KMAX variable and the 
number of states, the longer time and space the simulation will require. 
<P><B>Another example</B> 
<P>Let's assume this time we have a Gauss-Markov Process described by 
<P><IMG height=41 alt=displaymath281 
src="HP48G(X) Discrete Kalman Filter Simulator.files/img63.gif" width=402 
align=bottom> 
<P>
<P>The noise measurements will be taken at <IMG height=14 alt=tex2html_wrap181 
src="HP48G(X) Discrete Kalman Filter Simulator.files/img64.gif" width=32 
align=bottom> intervals of time, the measurement error will have a covariance 
<IMG height=14 alt=tex2html_wrap155 
src="HP48G(X) Discrete Kalman Filter Simulator.files/img43.gif" width=13 
align=bottom> of <IMG height=13 alt=tex2html_wrap160 
src="HP48G(X) Discrete Kalman Filter Simulator.files/img50.gif" width=7 
align=bottom> , and the measurement relationship <IMG height=13 
alt=tex2html_wrap153 
src="HP48G(X) Discrete Kalman Filter Simulator.files/img40.gif" width=16 
align=bottom> to <IMG height=9 alt=tex2html_wrap127 
src="HP48G(X) Discrete Kalman Filter Simulator.files/img19.gif" width=10 
align=bottom> is <IMG height=13 alt=tex2html_wrap160 
src="HP48G(X) Discrete Kalman Filter Simulator.files/img50.gif" width=7 
align=bottom> . The following is the input data: <IMG height=21 
alt=tex2html_wrap187 
src="HP48G(X) Discrete Kalman Filter Simulator.files/img65.gif" width=386 
align=bottom> and <IMG height=17 alt=tex2html_wrap188 
src="HP48G(X) Discrete Kalman Filter Simulator.files/img66.gif" width=58 
align=bottom> 
<P>The following is the <IMG height=13 alt=tex2html_wrap159 
src="HP48G(X) Discrete Kalman Filter Simulator.files/img49.gif" width=55 
align=bottom> program: 
<P><B>
<P>?[[ 1 ]] 'F' STO [[ 1.414 ]] 'G' STO [[ 1 ]] 'H' STO [[ 1 ]] 'W' STO .02 'T' 
STO [[ 0 ]] [[ 1 ]] 'R' STO 'XHM' STO [[ 1 ]] 'PM' STO [[ 0 ]] 'X' STO 50 'KMAX' 
STO 1 'EL' STO? 
<P>Some hints: </B>
<P>* Set your calculator to radians
<P>* For reasonable approximation, set the decimal places to 4 (FIX)
<P>* If you already have the covariance Q and/or the transition matrix, insert 
them into "Q" and "PHI" just before running "SIM-&gt;"
<P>* A reasonable "KMAX" is about 30
<P>* The "PPAR" that comes with the program should be present at all times
<P>* All parameters (i.e, F, G, etc) should be written in matrix form [[ ]]
<P>
<P><BR>
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<ADDRESS>
<CENTER>Now you can access the <A 
href="http://riccati.isu.edu/~martin/kalman/download.html">Download Page</A> 
<P>You may want to visit some <A 
href="http://riccati.isu.edu/~martin/kalman/links.html">Related Links</A> 
<P>
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