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theodolite.html
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<html>
<head>
<title>
THEODOLITE - Locating Atmospheric Events
</title>
</head>
<body bgcolor="#eeeeee" link="#cc0000" alink="#ff3300" vlink="#000055">
<h1 align = "center">
THEODOLITE <br> Locating Atmospheric Events
</h1>
<hr>
<p>
<b>THEODOLITE</b>
is a MATLAB library which
presents the problem of estimating the location of an event
which occurs in the sky, atmosphere, or the heavens, using nothing
but the reported angle of observation from several stations.
This is an example in which a nonlinear least squares solver is needed.
</p>
<p>
A <i>theodolite</i> is a tool for accurately measuring the angular
position of an event. It can be idealized as a pair of protractors,
one of which measures an angle in the local horizontal plane,
with an origin, say, pointing to the north. The second protractor
is used to measure the height of the observation.
</p>
<p>
When a missile is fired at a test facility, its trajectory was followed
by numerous theodolites at scattered locations. Measurements made by
the theodolites, taken at the same time, could be used to estimate the
actual location of the missile at that time. Since there were multiple
measurements available, and the measurements were all subject to some
error, it is natural to consider applying the least squares method to
the problem of determining an estimated location that minimizes the
sum of squared residuals.
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>THEODOLITE</b> is available in
<a href = "../../m_src/theodolite/theodolite.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../m_src/geometry/geometry.html">
GEOMETRY</a>,
a MATLAB library which
performs geometric calculations in 2, 3 and M dimensional space,
including the computation of angles, areas, containment, distances,
intersections, lengths, and volumes.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Charles Hall,<br>
Industrial Mathematics: A Course in Realism,<br>
American Mathematical Monthly,<br>
Volume 82, Number 6, June-July 1975, pages 651-659.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "line_par_point_dist_3d.m">line_par_point_dist_3d.m</a>,
determines the distance from a point in 3D to a line defined by
a parametric equation.
</li>
<li>
<a href = "r8vec_transpose_print.m">r8vec_transpose_print.m</a>,
prints the transpose of an R8VEC.
</li>
<li>
<a href = "theodolite_f.m">theodolite_f.m</a>,
a function which, given a proposed location XYZ for the event,
returns a vector F of the distance of the event to each line
defined by an observer's data.
</li>
<li>
<a href = "timestamp.m">timestamp.m</a>,
prints the current YMDHMS date as a time stamp.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "theodolite_test.m">theodolite_test.m</a>,
calls all the tests.
</li>
<li>
<a href = "theodolite_test_output.txt">theodolite_test_output.txt</a>,
the output file.
</li>
<li>
<a href = "theodolite_test01.m">theodolite_test01.m</a>,
solves a theodolite problem with 10 observers.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../m_src.html">
the MATLAB source codes</a>.
</p>
<hr>
<i>
Last modified on 04 May 2013.
</i>
<!-- John Burkardt -->
</body>
</html>