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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_215</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_214.html">< previous page</a></td> <td id="ebook_previous" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_215</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_216.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 215</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">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>a</i>2<i>p</i></sub></font><font face="Times New Roman, Times, Serif" size="3">. Substituting such an expression for <img src="d930a871af3a8255573f698084cd18fa.gif" border="0" alt="C0215-01.GIF" width="30" height="20" /> into Eq. (6.106) 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="3e76198787660af8e3d572a0852bef23.gif" border="0" alt="0215-01.GIF" width="294" height="21" /></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="e19d941d4511a1100ebccc6d374e8561.gif" border="0" alt="C0215-02.GIF" width="15" height="16" /> represents the actual accelerometer measurements accounting for all measurement errors. In a finite-dimensional model, the designer can hope to account for only the major sources of measurement error. 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="fdc083332fe9a3d7bfbfe0ae85c10494.gif" border="0" alt="0215-02.GIF" width="358" 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">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>a</i></sub></font><font face="Times New Roman, Times, Serif" size="3"> is a diagonal matrix representing uncompensated accelerometer 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>a</i></sub></font><font face="Times New Roman, Times, Serif" size="3"> represents uncompensated accelerometer bias, </font><font face="Symbol" size="3">d</font><font face="Times New Roman, Times, Serif" size="3">nl</font><font face="Times New Roman, Times, Serif" size="1"><sub><i>a</i></sub></font><font face="Times New Roman, Times, Serif" size="3"> represents uncompensated accelerometer nonlinearity, and </font><font face="Symbol" size="3">n</font><font face="Times New Roman, Times, Serif" size="1"><sub><i>a</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>a</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. (6.107) and (6.108) and linearizing results in the following equations for the actual navigation-frame specific force measurement and measurement error 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="2a3a8019e31113d308061728f61fd223.gif" border="0" alt="0215-03.GIF" width="390" 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="b067c35047fd6827d9be7dfed9e41cc7.gif" border="0" alt="0215-04.GIF" width="396" 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="d909a9b23d10cc4bdb9c45db9a8f222a.gif" border="0" alt="0215-05.GIF" width="372" 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">where <img src="e7d0d7ebbe16783ffa87c5ad10651d8f.gif" border="0" alt="C0215-03.GIF" width="129" height="20" /> accounts for error in the alignment process and f</font><font face="Times New Roman, Times, Serif" size="2"><sup><i>a</i></sup></font><font face="Times New Roman, Times, Serif" size="3"> is approximated by f</font><font face="Times New Roman, Times, Serif" size="2"><sup><i>p</i></sup></font><font face="Times New Roman, Times, Serif" size="3"> for a first-order expression. In the subsequent paragraphs, Eq. (6.99) and (6.111) are used to determine a linearized differential equation relating the various types of accelerometer measurement error to the time derivative of the velocity error.</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 time derivative of velocity error with respect to accelerometer bias is</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="e1684232e662f591b05108d67079d062.gif" border="0" alt="0215-06.GIF" width="317" height="38" /></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">Typically, </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>a</i></sub></font><font face="Times New Roman, Times, Serif" size="3"> is modeled as a random-walk variable <img src="53c6e76c900bfe48bac94053d6d402ea.gif" border="0" alt="C0215-04.GIF" width="192" 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">Letting </font><font face="Symbol" size="3">d</font><font face="Times New Roman, Times, Serif" size="3">A</font><font face="Times New Roman, Times, Serif" size="1"><sub><i>a</i></sub></font><font face="Times New Roman, Times, Serif" size="3"> = (</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>a</i></sub></font><font face="Times New Roman, Times, Serif" size="3"> - </font><font face="Symbol" size="3">d</font><font face="Times New Roman, Times, Serif" size="1"><sub><i>p</i>2<i>a</i></sub></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"><img src="eefc4fd219187caea098ec720a3fcb61.gif" border="0" alt="0215-07.GIF" width="344" height="56" /></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 auxiliary state composed of the accelerometer scale factor and misalignment matrix parameters to be</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="8de677954821ffb552a5fe8d1f88cc4d.gif" border="0" alt="0215-08.GIF" width="387" height="20" /></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_214.html">< previous page</a></td> <td id="ebook_next" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_215</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_216.html">next page ></a></td> </tr> </table> </body> </html>⌨️ 快捷键说明
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