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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_282</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_281.html">< previous page</a></td> <td id="ebook_previous" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_282</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_283.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 282</font></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">Sec. 6.8.1.1, the knowledge of the baseline vectors in body and tangent frames allows the computation of the coordinate frame transformation matrix as</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="a0d08d35ec01fa597a5d977c32f3cd87.gif" border="0" alt="0282-01.GIF" width="289" height="18" /></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 <img src="93db5b6a26d7308ba8059dc6acbbf8d3.gif" border="0" alt="C0282-01.GIF" width="136" height="20" /> and <img src="1b07c5d86413a54c25462a20a5c88d28.gif" border="0" alt="C0282-02.GIF" width="132" height="22" />. This calculation of <img src="9d8c59183b4da955f5c95f0c1125f4a9.gif" border="0" alt="C0282-03.GIF" width="26" height="18" /> (possibly including orthogonalization) provides the direction-cosine matrix or would allow calculation of the quaternion or Euler angle parameters, depending on the system design requirements.</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">Two special cases are of note. First, if the body-frame baseline vectors corresponded to [</font><font face="Symbol" size="3"><i>a</i></font><font face="Times New Roman, Times, Serif" size="3">, 0, 0] and [0, </font><font face="Symbol" size="3"><i>b</i></font><font face="Times New Roman, Times, Serif" size="3">, 0], 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="365d8e56944a286ac96a55247d6bdd1a.gif" border="0" alt="0282-02.GIF" width="314" height="64" /></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 special case in which </font><font face="Symbol" size="3"><i>a</i></font><font face="Times New Roman, Times, Serif" size="3"> = </font><font face="Symbol" size="3"><i>b</i></font><font face="Times New Roman, Times, Serif" size="3"> = 1, R</font><font face="Times New Roman, Times, Serif" size="1"><sub><i>b</i>2<i>t</i></sub></font><font face="Times New Roman, Times, Serif" size="3"> = B</font><font face="Times New Roman, Times, Serif" size="2"><sup><i>e</i></sup></font><font face="Times New Roman, Times, Serif" size="3">. Second, assume that <img src="95cd048a8c6c553171b21a0f73387e39.gif" border="0" alt="C0282-04.GIF" width="77" height="20" /> and <img src="f882e70fc56d00c1aa780af33680916c.gif" border="0" alt="C0282-05.GIF" width="202" height="19" />. 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="b77a0f2fe59b8ce4e2325e7e52292a87.gif" border="0" alt="0282-03.GIF" width="390" height="55" /></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">Therefore</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="db641d9f497f2e904006b1faddae187b.gif" border="0" alt="0282-04.GIF" width="316" height="17" /></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="6713b77ebcc0a5d5c1b90f7f9cf6992c.gif" border="0" alt="0282-05.GIF" width="314" height="54" /></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 arctan2 is the four-quadrant inverse tangent function. Although this calculation is based on the assumption that the baseline vector b</font><font face="Times New Roman, Times, Serif" size="1"><sub>1</sub></font><font face="Times New Roman, Times, Serif" size="3"> defines the vehicle <i>u</i> axis, it is insensitive to knowledge of the length of the baseline vector. This length does affect the noise sensitivity. Define an intermediate vector <img src="2693b6844897b2bc0a9dd0a0a647aba6.gif" border="0" alt="C0282-06.GIF" width="17" height="17" /> as the tangent-plane <img src="971c290c21cb0ffca09fd6d7d6b2e61a.gif" border="0" alt="C0282-07.GIF" width="17" height="18" /> vector rotated through the heading and pitch transformations that are known based on Eqs. (7.91) and (7.92):</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="3e56e092f6d36d6ae88bc7d5d1de31e3.gif" border="0" alt="0282-06.GIF" width="164" height="20" /></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">Then the transformation to body frame is completed by the roll angle rotation:</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="f1a29fa9f5ac94dfb5ea89641ff79d84.gif" border="0" alt="0282-07.GIF" width="378" height="56" /></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_281.html">< previous page</a></td> <td id="ebook_next" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_282</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_283.html">next page ></a></td> </tr> </table> </body> </html>⌨️ 快捷键说明
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