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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_54</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_53.html">< previous page</a></td> <td id="ebook_previous" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_54</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_55.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 54</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="fdbdabe78510e11b624daa15690ebd99.gif" border="0" alt="0054-01.GIF" width="444" height="354" /></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2.14<br />Quaternion聽drift聽error聽versus聽angle聽magnitude聽for聽first-聽through聽sixth-order聽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">through </font><font face="Symbol" size="3"><i>a</i></font><font face="Times New Roman, Times, Serif" size="3"> interact with the present angular velocity </font><font face="Symbol" size="3"><i>w</i></font><font face="Times New Roman, Times, Serif" size="3"> to produce the present rate </font><font face="Symbol" size="3"><i>a</i></font><font face="Times New Roman, Times, Serif" size="3">). For compatibility with the previously presented direction-cosine algorithms, </font><font face="Symbol" size="3"><i>a</i></font><font face="Times New Roman, Times, Serif" size="3"> is used in place of </font><font face="Symbol" size="3"><i>u</i></font><font face="Times New Roman, Times, Serif" size="3">. For compatibility with the previously presented quaternion algorithms </font><font face="Symbol" size="3"><i>a</i></font><font face="Times New Roman, Times, Serif" size="3"> is used in place of </font><font face="Symbol" size="3"><i>J</i></font><font face="Times New Roman, Times, Serif" size="3">.</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 closed-form discrete-time solutions to the direction-cosine and the quaternion approaches lend themselves to implementation at two different sample rates. Equation (2.104) is implemented at the highest rate. The rate is selected high enough to ensure the accuracy of </font><font face="Symbol" size="3"><i>a</i></font><font face="Times New Roman, Times, Serif" size="3">. In Ref. 130 it is shown that, to (approximately) third order, Eq. (2.104) can be implemented by the following equations:</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="87c09856747c69bb27981f1b9e5b3c83.gif" border="0" alt="0054-02.GIF" width="279" 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="3a387cf0c270f2372da90fae7009c6d6.gif" border="0" alt="0054-03.GIF" width="285" height="34" /></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="28bb1fa4b008fe19b36cbbd5bbc646c0.gif" border="0" alt="0054-04.GIF" width="279" 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">Accuracy can be evaluated, for example, in the presence of vibration [130] or coning motion [130, 138]. The direction-cosine update [Eq. (2.63)] or quaternion update [Eq. (2.85)] is implemented at a lower rate. This rate is selected high enough that ||</font><font face="Symbol" size="3"><i>a</i></font><font face="Times New Roman, Times, Serif" size="3">|| < 1 under worst-case conditions, as analyzed in Sec. 2.5.3.4.</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_53.html">< previous page</a></td> <td id="ebook_next" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_54</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_55.html">next page ></a></td> </tr> </table> </body> </html>⌨️ 快捷键说明
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