📄 page_217.html
字号:
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN" "http://www.w3.org/TR/html4/strict.dtd"> <html> <head> <title>page_217</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_216.html">< previous page</a></td> <td id="ebook_previous" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_217</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_218.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 217</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">The platform-frame to gyro-frame transformation R</font><font face="Times New Roman, Times, Serif" size="1"><sub><i>p</i>2<i>g</i></sub></font><font face="Times New Roman, Times, Serif" size="3"> is a nonorthogonal transformation that accounts for gyro misalignment. This rotation has the form</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="68ab5903b527b4baedcad5081be0c5b8.gif" border="0" alt="0217-01.GIF" width="337" 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="4a3ef9edd08fc1b9dd4f025652b36f3c.gif" border="0" alt="0217-02.GIF" width="337" height="62" /></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 this notation, <i>g</i></font><i><font face="Times New Roman, Times, Serif" size="1"><sub>pr</sub></font></i><font face="Times New Roman, Times, Serif" size="1"><sub></sub></font><font face="Times New Roman, Times, Serif" size="3"> represents the positive rotation angle (in radians) about the platform <i>r</i> axis from the platform <i>p-r</i> plane to the gyro <i>p</i> axis. This results in platform <i>q</i> rotation's being measured positively by the <i>p</i> gyro. The other terms are defined similarly. The term R</font><font face="Times New Roman, Times, Serif" size="1"><sub><i>g</i>2<i>p</i></sub></font><font face="Times New Roman, Times, Serif" size="3"> = (R</font><font face="Times New Roman, Times, Serif" size="1"><sub><i>p</i>2<i>g</i></sub></font><font face="Times New Roman, Times, Serif" size="3">)</font><font face="Times New Roman, Times, Serif" size="2"><sup>-1</sup></font><font face="Times New Roman, Times, Serif" size="3">, which can be shown by direct multiplication to yield</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="3a4751ae12d15af457c2c659a4a82b84.gif" border="0" alt="0217-03.GIF" width="293" 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">to first order.</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 computed angular rate in platform coordinates is described 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="1981f8e9c8bcdcdc9cce8174ba322778.gif" border="0" alt="0217-04.GIF" width="284" 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 accelerometer-frame to platform-frame transformation <img src="25ecd8d43d93ef8e3400951f180e038d.gif" border="0" alt="RG2P.GIF" width="31" height="22" /> is often assumed to be an identity, but could also have off-diagonal elements determined through an alignment process. This rotation matrix has the same structure as that defined for R</font><font face="Times New Roman, Times, Serif" size="1"><sub><i>g</i>2<i>p</i></sub></font><font face="Times New Roman, Times, Serif" size="3">. Substituting the expression for <img src="25ecd8d43d93ef8e3400951f180e038d.gif" border="0" alt="RG2P.GIF" width="31" height="22" /> into Eq. (6.124) yields</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="11f4f2270127c5f6b9c75b6540d254b7.gif" border="0" alt="0217-05.GIF" width="301" 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">The term <img src="ef0f9a0be475c1588c0d13a209c218a7.gif" border="0" alt="C0217-01.GIF" width="23" height="22" /> represents the actual gyro measurements accounting for all measurement errors. To develop a finite-dimensional error model, only bias, scale-factor, noise, and g-sensitive errors will considered. Let</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="f61d9c009930b92f9f2b17535ce769e8.gif" border="0" alt="0217-06.GIF" width="361" 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">where </font><font face="Symbol" size="3">d</font><font face="Times New Roman, Times, Serif" size="3">SF</font><font face="Times New Roman, Times, Serif" size="1"><sub><i>g</i></sub></font><font face="Times New Roman, Times, Serif" size="3"> is a diagonal matrix representing uncompensated gyro scale-factor error, </font><font face="Symbol" size="3">d</font><font face="Times New Roman, Times, Serif" size="3">b</font><font face="Times New Roman, Times, Serif" size="1"><sub><i>g</i></sub></font><font face="Times New Roman, Times, Serif" size="3"> represents uncompensated gyro bias, </font><font face="Symbol" size="3">d</font><font face="Times New Roman, Times, Serif" size="3">k</font><font face="Times New Roman, Times, Serif" size="1"><sub><i>g</i></sub></font><font face="Times New Roman, Times, Serif" size="3"> represents uncompensated gyro g sensitivity, and </font><font face="Symbol" size="3">n</font><font face="Times New Roman, Times, Serif" size="1"><sub><i>g</i></sub></font><font face="Times New Roman, Times, Serif" size="3"> represents random measurement noise. For dynamic modeling, </font><font face="Symbol" size="3">n</font><font face="Times New Roman, Times, Serif" size="1"><sub><i>g</i></sub></font><font face="Times New Roman, Times, Serif" size="3"> may be either a white or a colored vector noise process.</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">Combining Eqs. (6.125) and (6.126) and linearizing results in the following equations for the actual platform-frame angular rate measurement and measurement error:</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="6bbd6b863ff8c7ec3546e98f188468ca.gif" border="0" alt="0217-07.GIF" width="401" 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"><img src="130148fed44199f25e475b3d472111b5.gif" border="0" alt="0217-08.GIF" width="406" 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"><img src="7c7105e6e8becae90845dff86f51c5a5.gif" border="0" alt="0217-09.GIF" width="375" height="21" /></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_216.html">< previous page</a></td> <td id="ebook_next" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_217</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_218.html">next page ></a></td> </tr> </table> </body> </html>⌨️ 快捷键说明
复制代码
Ctrl + C
搜索代码
Ctrl + F
全屏模式
F11
切换主题
Ctrl + Shift + D
显示快捷键
?
增大字号
Ctrl + =
减小字号
Ctrl + -