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           "http://www.w3.org/Math/DTD/mathml2/mathml2.dtd">

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<h1>Ridgy software and algorithms</h1>
<h3>Extension to the observation model</h3>
The new landmark design and recognition gives the distance <i>d</i> to the landmark, 
the angle <i>&theta;</i> between the robot and the center of the landmark and 
the angle <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
	<mover>
		<mi>&alpha;</mi><mo>~</mo>
	</mover>
</math> between a line <i>l</i>, from the center of the robot to the center of the landmark, and 
the landmark plane normal vector. <br />
Using the fact that the height <i>h</i> of an observed landmark is constant for any angle of the landmark plane 
(for a constant distance <i>d</i>), and the width <i>w</i> variates with the angle, 
the observed angle <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML">
	<mover>
		<mi>&alpha;</mi><mo>~</mo>
	</mover>
</math> of the landmark plane can be calculated as:

<math display="block" xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
  <mover>
          <mi>&alpha;</mi>
        <mo>~</mo>
  </mover>
  <mo>=</mo>
  <mi>arccos</mi><mo>&ApplyFunction;</mo>
  <mfrac>
    <mrow>
      <mi>w</mi>
    </mrow>
    <mrow>
      <mi>h</mi>
    </mrow>
  </mfrac>
</mrow>
</math>


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