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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN" "http://www.w3.org/TR/html4/strict.dtd"> <html> <head> <title>page_51</title> <link rel="stylesheet" href="reset.css" type="text/css" media="all"> <meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /> </head> <body> <table summary="top nav" border="0" width="100%"> <tr> <td align="left" width="30%" style="background: #EEF3E2"><a style="color: blue; font-size: 120%; font-weight: bold; text-decoration: none; font-family: verdana;" href="page_50.html">< previous page</a></td> <td id="ebook_previous" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_51</strong></td> <td align="right" width="30%" style="background: #EEF3E2"><a style="color: blue; font-size: 120%; font-weight: bold; text-decoration: none; font-family: verdana;" href="page_52.html">next page ></a></td> </tr> <tr> <td id="ebook_page" align="left" colspan="3" style="background: #ffffff; padding: 20px;"> <table border="0" width="100%" cellpadding="0"><tr><td align="center"> <table border="0" cellpadding="2" cellspacing="0" width="100%"><tr><td align="left"></td> <td align="right"></td> </tr></table></td></tr><tr><td align="left"><p></p><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="right"><font face="Times New Roman, Times, Serif" size="2" color="#FF0000">Page 51</font></td></tr></table><table cellpadding="0" cellspacing="0" border="0" width="100%"><tr><td height="12"></td></tr><tr><td><table cellspacing="0" width="629" cellpadding="4"><tr><td colspan="7" valign="top"><font face="Times New Roman, Times, Serif" size="2">TABLE 2.3 Coefficients for Approximate Direction-Cosine Update for Algorithms of Orders One through Six</font></td></tr><tr><td valign="top"></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2">First</font></td></tr></table></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2">Second</font></td></tr></table></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2">Third</font></td></tr></table></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2">Fourth</font></td></tr></table></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2">Fifth</font></td></tr></table></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2">Sixth</font></td></tr></table></td></tr><tr><td valign="top"><font face="Times New Roman, Times, Serif" size="2"><i>f</i></font><font face="Times New Roman, Times, Serif" size="1"><sub>1</sub></font></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2">1</font></td></tr></table></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2">1</font></td></tr></table></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2">1-</font><font face="Symbol" size="2"><i>s</i></font><font face="Times New Roman, Times, Serif" size="2">2/6</font></td></tr></table></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2">1-</font><font face="Symbol" size="2"><i>s</i></font><font face="Times New Roman, Times, Serif" size="2"><sup>2</sup>/6</font></td></tr></table></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2">1-</font><font face="Symbol" size="2"><i>s</i></font><font face="Times New Roman, Times, Serif" size="2"><sup>2</sup>/6</font></td></tr></table></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2">1-</font><font face="Symbol" size="2"><i>s</i></font><font face="Times New Roman, Times, Serif" size="2"><sup>2</sup>/6+</font><font face="Symbol" size="2"><i>s</i></font><font face="Times New Roman, Times, Serif" size="2"><sup>4</sup>/120</font></td></tr></table></td></tr><tr><td valign="top"><font face="Times New Roman, Times, Serif" size="2"><i>f</i></font><font face="Times New Roman, Times, Serif" size="1"><sub>2</sub></font></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2">0</font></td></tr></table></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2">0.5</font></td></tr></table></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2">0.5</font></td></tr></table></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2">0.5-</font><font face="Symbol" size="2"><i>s</i></font><font face="Times New Roman, Times, Serif" size="2"><sup>2</sup>/24</font></td></tr></table></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2">0.5-</font><font face="Symbol" size="2"><i>s</i></font><font face="Times New Roman, Times, Serif" size="2"><sup>2</sup>/24</font></td></tr></table></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2">0.5-</font><font face="Symbol" size="2"><i>s</i></font><font face="Times New Roman, Times, Serif" size="2"><sup>2</sup>/24+</font><font face="Symbol" size="2"><i>s</i></font><font face="Times New Roman, Times, Serif" size="2"><sup>4</sup>/720</font></td></tr></table></td></tr></table></td></tr></table><br /><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3">The first line represents the drift error. The second line represents the scale and the skew errors, which will be zero if <img src="c7964d70a8c372381587469ddb438545.gif" border="0" alt="RCIRC.GIF" width="16" height="18" /> has been orthonormalized. The drift error will be calculated as the rms value of the upper triangular portion of P. Since (1/||</font><font face="Symbol" size="3"><i>u</i></font><font face="Times New Roman, Times, Serif" size="3">||)</font><font face="Symbol" size="3"><i>u</i></font><font face="Times New Roman, Times, Serif" size="3"> a unit vector and </font><font face="Symbol" size="3">隆</font><font face="Times New Roman, Times, Serif" size="3"> = [</font><font face="Symbol" size="3"><i>u</i>麓</font><font face="Times New Roman, Times, Serif" size="3">], the magnitude of the drift error is given by</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3"><img src="d2bd2e85cd5e7120a42370b9578ba3ba.gif" border="0" alt="0051-01.GIF" width="392" height="19" /></font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3">Table 2.3 displays the expressions for <i>f</i></font><font face="Times New Roman, Times, Serif" size="1"><sub>1</sub></font><font face="Times New Roman, Times, Serif" size="3">, and <i>f</i></font><font face="Times New Roman, Times, Serif" size="1"><sub>2</sub></font><font face="Times New Roman, Times, Serif" size="3"> for various order algorithms [138], where </font><font face="Symbol" size="3"><i>s</i></font><font face="Times New Roman, Times, Serif" size="3"> = ||</font><font face="Symbol" size="3"><i>u</i></font><font face="Times New Roman, Times, Serif" size="3">||. Figure 2.13 plots <i>D</i>(</font><font face="Symbol" size="3"><i>s</i></font><font face="Times New Roman, Times, Serif" size="3">) for first- through sixth-order algorithms. Note that the figure indicates the error incurred just because of the approximate calculation of </font><font face="Symbol" size="3">L</font><font face="Times New Roman, Times, Serif" size="3">. Additional error incurred because of approximations involved in the calculation of </font><font face="Symbol" size="3"><i>u</i></font><font face="Times New Roman, Times, Serif" size="3"> are discussed below in this section. The figure indicates that there are large benefits in picking a third- or a fifth-order algorithm relative to second- or fourth-order algorithms. Also, there is a substantial benefit to selecting an update rate for </font><font face="Symbol" size="3">L</font><font face="Times New Roman, Times, Serif" size="3"> high enough that the worst-case max(||</font><font face="Symbol" size="3"><i>u</i></font><font face="Times New Roman, Times, Serif" size="3">||) is small.</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3">In the quaternion approach, the transformation valid at time <i>t</i></font><i><font face="Times New Roman, Times, Serif" size="1"><sub>k</sub></font></i><font face="Times New Roman, Times, Serif" size="1"><sub></sub></font><font face="Times New Roman, Times, Serif" size="3"> is</font><font face="Times New Roman, Times, Serif" size="3" color="#FFFF00"></font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3"><img src="90237d4cccc916424cd9c277a27cba64.gif" border="0" alt="0051-02.GIF" width="460" height="41" /></font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3"><img src="518b06e81104b9ce93d78660fb546450.gif" border="0" alt="0051-03.GIF" width="428" height="127" /></font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3"><img src="743cba3c7761e219c03bd9eae1fd8b99.gif" border="0" alt="0051-04.GIF" width="428" height="106" /></font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table></td></tr></table><p><font size="0"></font></p>聽 </td> </tr> <tr> <td align="left" width="30%" style="background: #EEF3E2"><a style="color: blue; font-size: 120%; font-weight: bold; text-decoration: none; font-family: verdana;" href="page_50.html">< previous page</a></td> <td id="ebook_next" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_51</strong></td> <td align="right" width="30%" style="background: #EEF3E2"><a style="color: blue; font-size: 120%; font-weight: bold; text-decoration: none; font-family: verdana;" href="page_52.html">next page ></a></td> </tr> </table> </body> </html>⌨️ 快捷键说明
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