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this book can help you to get a better performance in the gps development

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  <td><font face="Times New Roman, Times, Serif" size="3"><img src="8c40c3e5ef5b8a723a30b9eef156a391.gif" border="0" alt="0300-02.GIF" width="461" height="35" /></font></td>
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  <td><font face="Times New Roman, Times, Serif" size="3">The singular value decomposition of a matrix A </font><font face="Symbol" size="3">脦</font><font face="Times New Roman, Times, Serif" size="3"> <i>R</i></font><i><font face="Times New Roman, Times, Serif" size="2"><sup>m</sup></font></i><font face="Times New Roman, Times, Serif" size="2"><sup>脳<i>n</i></sup></font><font face="Times New Roman, Times, Serif" size="3"> is defined as A = U</font><font face="Symbol" size="3">S</font><font face="Times New Roman, Times, Serif" size="3">V</font><font face="Times New Roman, Times, Serif" size="3">, where U </font><font face="Symbol" size="3">脦</font><font face="Times New Roman, Times, Serif" size="3"> <i>R</i></font><i><font face="Times New Roman, Times, Serif" size="2"><sup>m</sup></font></i><font face="Times New Roman, Times, Serif" size="2"><sup>脳<i>m</i></sup></font><font face="Times New Roman, Times, Serif" size="3"> and V </font><font face="Symbol" size="3">脦</font><font face="Times New Roman, Times, Serif" size="3"> <i>R</i></font><i><font face="Times New Roman, Times, Serif" size="2"><sup>n</sup></font></i><font face="Times New Roman, Times, Serif" size="2"><sup>脳<i>n</i></sup></font><font face="Times New Roman, Times, Serif" size="3"> are orthogonal matrices and </font><font face="Symbol" size="3">S</font><font face="Times New Roman, Times, Serif" size="3"></font><font face="Symbol" size="3">脦</font><font face="Times New Roman, Times, Serif" size="3"> <i>R</i></font><i><font face="Times New Roman, Times, Serif" size="2"><sup>m</sup></font></i><font face="Times New Roman, Times, Serif" size="2"><sup>脳<i>n</i></sup></font><font face="Times New Roman, Times, Serif" size="3"> is a diagonal matrix. The diagonal of </font><font face="Symbol" size="3">S</font><font face="Times New Roman, Times, Serif" size="3"> is defined as (</font><font face="Symbol" size="3">s</font><font face="Times New Roman, Times, Serif" size="1"><sub>1</sub></font><font face="Times New Roman, Times, Serif" size="3">, </font><font face="Symbol" size="3">s</font><font face="Times New Roman, Times, Serif" size="1"><sub>2</sub></font><font face="Times New Roman, Times, Serif" size="3">,聽.聽.聽.聽, </font><font face="Symbol" size="3">s</font><font face="Times New Roman, Times, Serif" size="1"><sub><i>p</i></sub></font><font face="Times New Roman, Times, Serif" size="3">) where <i>p</i> = min(<i>m, n</i>). The diagonal elements of </font><font face="Symbol" size="3">S</font><font face="Times New Roman, Times, Serif" size="3"> are ordered so that </font><font face="Symbol" size="3">s</font><font face="Times New Roman, Times, Serif" size="1"><sub>1 </sub></font><font face="Times New Roman, Times, Serif" size="3">&gt; </font><font face="Symbol" size="3">s</font><font face="Times New Roman, Times, Serif" size="1"><sub>2 </sub></font><font face="Times New Roman, Times, Serif" size="3">&gt;聽路聽路聽路 &gt; </font><font face="Symbol" size="3">s</font><font face="Times New Roman, Times, Serif" size="1"><sub><i>p</i></sub></font><font face="Times New Roman, Times, Serif" size="3"></font><font face="Symbol" size="3">鲁</font><font face="Times New Roman, Times, Serif" size="3"> 0. The </font><font face="Symbol" size="3">s</font><font face="Times New Roman, Times, Serif" size="1"><sub><i>i</i></sub></font><font face="Times New Roman, Times, Serif" size="3"> are the singular values of the matrix A. The rank of A is the integer <i>d</i> such that </font><font face="Symbol" size="3">s</font><font face="Times New Roman, Times, Serif" size="1"><sub><i>i</i></sub></font><font face="Times New Roman, Times, Serif" size="3"> = 0 for <i>p</i> </font><font face="Symbol" size="3">拢</font><font face="Times New Roman, Times, Serif" size="3"> <i>i </i>&gt; <i>d</i>. The first <i>d</i> columns of U form an orthogonal basis for the range space of A. The last <i>n - d</i> rows of V form an orthogonal basis for the null space of A. Additional properties of the singular value decomposition and algorithms for its computation can be found in Ref. 57.</font></td>
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  <td><font face="Times New Roman, Times, Serif" size="3">If the matrix A is orthogonal, then </font><font face="Symbol" size="3">s</font><font face="Times New Roman, Times, Serif" size="1"><sub>1</sub></font><font face="Times New Roman, Times, Serif" size="3"> = </font><font face="Symbol" size="3">s</font><font face="Times New Roman, Times, Serif" size="1"><sub>2</sub></font><font face="Times New Roman, Times, Serif" size="3"> =聽路聽路聽路 = </font><font face="Symbol" size="3">s</font><font face="Times New Roman, Times, Serif" size="1"><sub><i>p</i></sub></font><font face="Times New Roman, Times, Serif" size="3"> = 1. If 脗 = U</font><font face="Symbol" size="3">S</font><font face="Times New Roman, Times, Serif" size="3">V</font><font face="Times New Roman, Times, Serif" size="3"> is a computed version of A and is not orthogonal because of numeric errors, it can be orthogonalized as</font></td>
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  <td><font face="Times New Roman, Times, Serif" size="3"><img src="3b97b90854fe1589f59f74bb75cd3149.gif" border="0" alt="0300-03.GIF" width="271" height="20" /></font></td>
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  <td><font face="Times New Roman, Times, Serif" size="3">This singular value decomposition approach to orthogonalization is completely equivalent to the traditional orthogonalization approach [18, 40] calculated as</font></td>
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  <td><font face="Times New Roman, Times, Serif" size="3"><img src="953d50a3cb5d977ef3bcab776b5b50c2.gif" border="0" alt="0300-04.GIF" width="334" height="20" /></font></td>
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  <td><font face="Times New Roman, Times, Serif" size="3">since</font><font face="Times New Roman, Times, Serif" size="3" color="#FFFF00"></font></td>
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  <td><font face="Times New Roman, Times, Serif" size="3"><img src="d3f949e3b264506910e97981ae84a2fb.gif" border="0" alt="0300-05.GIF" width="310" height="20" /></font></td>
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  <td><font face="Times New Roman, Times, Serif" size="3"><img src="65f9fdd00963d979d32cf99bf7a79798.gif" border="0" alt="0300-06.GIF" width="312" height="20" /></font></td>
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  <td><font face="Times New Roman, Times, Serif" size="3"><img src="066d02bc77e3e338677bdff7a1ded9b9.gif" border="0" alt="0300-07.GIF" width="312" height="19" /></font></td>
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