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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_52</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_51.html">< previous page</a></td> <td id="ebook_previous" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_52</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_53.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 52</font></td></tr></table><table border="0" cellspacing="0" cellpadding="0" width="100%"><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 align="center"><font face="Times New Roman, Times, Serif" size="3"><img src="0faf7a665766127049650f045c2fae2e.gif" border="0" alt="0052-01.GIF" width="445" height="355" /></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" width="100%"><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 align="center"><font face="Times New Roman, Times, Serif" size="2">Figure聽2.13<br />Direction-cosine聽drift聽error聽versus聽angle聽magnitude聽for聽first-聽through聽sixth-order<br />algorithms.</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">Define the quaternions</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="8f85009f297fb53e833e144be5b962da.gif" border="0" alt="0052-02.GIF" width="299" height="65" /></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">where </font><font face="Symbol" size="3">n</font><font face="Times New Roman, Times, Serif" size="3"> = ||</font><font face="Symbol" size="3"><i>J</i></font><font face="Times New Roman, Times, Serif" size="3">||, <i>f</i></font><i><font face="Times New Roman, Times, Serif" size="1"><sub>s</sub></font></i><font face="Times New Roman, Times, Serif" size="1"><sub></sub></font><font face="Times New Roman, Times, Serif" size="3">(</font><font face="Symbol" size="3">n</font><font face="Times New Roman, Times, Serif" size="3">) </font><font face="Symbol" size="3">禄</font><font face="Times New Roman, Times, Serif" size="3"> {[sin(</font><font face="Symbol" size="3">m</font><font face="Times New Roman, Times, Serif" size="3">/2)]/</font><font face="Symbol" size="3">n</font><font face="Times New Roman, Times, Serif" size="3">} and <i>f</i></font><i><font face="Times New Roman, Times, Serif" size="1"><sub>c</sub></font></i><font face="Times New Roman, Times, Serif" size="1"><sub></sub></font><font face="Times New Roman, Times, Serif" size="3">(</font><font face="Symbol" size="3">n</font><font face="Times New Roman, Times, Serif" size="3">/2) </font><font face="Symbol" size="3">禄</font><font face="Times New Roman, Times, Serif" size="3"> cos(</font><font face="Symbol" size="3">n</font><font face="Times New Roman, Times, Serif" size="3">/2). The quaternion r represents the transformation of the quaternion b between the two time instants that are of interest. The objective here is to evaluate the error incurred in this transformation when r is replaced by <img src="22901f59ff1e038421ba7a0d983348f7.gif" border="0" alt="C0052-01.GIF" width="13" height="15" />. Let R</font><font face="Times New Roman, Times, Serif" size="1"><sub><i>b</i></sub></font><font face="Times New Roman, Times, Serif" size="3">(<i>k</i>) denote the direction-cosine matrix corresponding to quaternion b at time instant <i>k</i>. Also, define <img src="519ad79b60d688465526ad474df32fb8.gif" border="0" alt="C0052-02.GIF" width="61" height="15" />. Then</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="dfbb28b8ef1d2c4a94ddbbea95854c3c.gif" border="0" alt="0052-03.GIF" width="364" 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"><img src="6593194e07c042b1e5d1676b5b8fa031.gif" border="0" alt="0052-04.GIF" width="364" height="22" /></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="4c629868f3dcf8bec3d62cd6a1fb15cf.gif" border="0" alt="0052-05.GIF" width="303" height="24" /></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">The quaternion yields an orthogonal direction-cosine matrix by design. If the direction-cosine matrix calculation includes normalization, as does the</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></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_51.html">< previous page</a></td> <td id="ebook_next" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_52</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_53.html">next page ></a></td> </tr> </table> </body> </html>⌨️ 快捷键说明
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